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OF  THE 

UNIVERSITY  OF  CALIFORNIA, 

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UNIVERSITY  OF  CALIFORNIA 

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Received N.QV...1.4..1.91.1 

^cessions  No.    &  f  Z          Book  m_/ 


SCIENTIFIC  MEMOIRS 

EDITED    BY 

J.  S.  AMES,  PH.D. 

PROFESSOR   OF   PHYSICS    IN   JOHNS    HOPKINS    UNIVERSITY 


XV 
THE  LAWS  OF   RADIATION  AND  ABSORPTION 


THE  LAWS 

OF 

RADIATION  AND  ABSORPTION 

MEMOIRS  BY    PROVOST,  STEWART,  KIRCHHOFF, 
AND  KIRCHHOFF  AND  BUNSEN. 


TRANSLATED   AND    EDITED    BY 

D.  B.  BRACE,  PH.D. 

PROFESSOR  OF   PHYSICS   IN   THE    UNIVERSITY  OF   NEBRASKA. 


NEW  YORK  •:•  CINCINNATI  -:•  CHICAGO 

AMEEICAN  BOOK  COMPANY 


COPYEIGHT,   1901,   BY 

AMERICAN  BOOK  COMPANY. 


Entered  at  Stationers''  Hall,  London. 

Radiation  and  Absorption. 
W.  P.  i 


\  \ 


PREFACE. 

THE  attempt  of  Prevost  to  explain  the  experiments  of  Pictet, 
of  the  apparent  concentration  of  cold  at  the  focus  of  a  mirror, 
without  attributing  the  quality  of  radiation  to  cold,  as  assumed 
by  Pictet,  lead  him  to  the  enunciation  of  the  very  important 
principle  which  he  called  the  movable  equilibrium  of  heat,  now 
designated  as  the  theory  of  exchanges.  Prevost,  who  was  a  dis- 
ciple of  le  Sage,  and  who  had  issued,  with  many  additions,  his 
memoirs,  assumed,  in  addition  to  a  corpuscular  fluid  caloric,  a 
free  corpuscular  radiant  caloric,  the  equal  interchange  of  which 
between  neighboring  free  spaces,  constituted  heat  equilibrium. 
Any  interference  with  this  equilibrium  will  be  reestablished  by 
the  inequalities  of  the  exchanges.  On  this  principle  he  was  able 
to  explain  the  apparent  concentration  of  cold  and  also  to  show 
the  inadmissibility  of  cold  as  an  agent  susceptible  of  radiation. 
He  was  careful,  however,  to  fortify  his  principle  by  showing  that 
the  same  results  would  follow  on  the  then  distrusted  hypothesis 
of  undulatory  exchanges,  which  has  been  adopted  by  his  suc- 
cessors. Later  experimenters,  particularly  Leslie  and  De  la 
Provastaye  and  Desains,  confirmed  the  theory  and  also  showed 
in  many  instances  quantitative  relations  between  radiation  and 
absorption.  But  the  most  important  advance  was  made  by  Bal- 
four  Stewart  in  establishing,  not  only  a  quantitative  relation, 
but  also  a  qualitative  or  selective  one.  By  the  introduction  of 
his  ingenious  idea  of  an  impervious  radiating  inclosure  he 
demonstrated  the  equality  between  the  emissive  and  the  absorp- 
tive power  of  any  wave  length.  We  owe  to  Kirchhoff,  however, 
the  first  rigorous  proof  of  the  celebrated  law  (usually  designated 
on  the  Continent  as  KirchhofFs  law)  of  the  emission  and  absorp- 
tion of  light  and  heat,  and  the  application  of  the  same  by  both 
Kirchhoff  and  Bunsen  to  Spectrum  Analysis.  The  radiation 
of  solids  and  liquids  and  gases  follows  the  law  exactly  when  the 
conditions  upon  which  he  founded  it  are  rigorously  fulfilled, 
namely,  the  complete  transformation  from  one  to  the  other  of 

222515 


PREFACE. 

radiant  energy  and  their  intrinsic  heat.  "We  now  know  that 
most  radiations  from  gases  are  not  exclusively  thermal,  but  that 
the  substances,  cited  by  Kirchhoff  and  Bunsen,  also  give  off  so 
called  chemical  and  electrical  and  fluorescent  radiations  which 
Kirchhoff  excluded  in  the  proof  of  his  law.  In  fact  none  of  the 
gases  giving  line  spectra  at  temperatures  heretofore  used  do  so 
by  simple  thermal  radiation,  but  essentially  by  luminescent 
actions  (chemical,  electrical,  and  photogenic),  so  that  we  cannot, 
in  general,  apply  the  law  of  Kirchhoff  of  the  proportionality 
between  radiation  and  absorption  to  either  terrestrial  or  celes- 
tial substances.  In  these  cases  the  principle  of  resonance  usually 
holds,  since  in  luminescence  the  radiation  of  line  spectra  is 
accompanied  by  selective  absorption  of  the  same  spectral  lines, 
so  that  the  law  may  be  used  qualitatively,  which  is  in  ftict  the 
way  Kirchhoff  and  Bunsen  actually  attempted  to  confirm  it. 
The  formulation  of  the  complete  law  for  radiations  of  a  Hack 
body  is  only  given  in  part  by  Kirchhoff.  The  formula  of  Wien, 
and  more  particularly  the  most  recent  one  of  Planck,  deduced 
on  theoretical  grounds,  approximates  closely  the  latest  observa- 
tions on  a  black  body  at  different  temperatures  and  over  differ- 
ent wave  lengths. 

D.  B.  BRACE. 
University  of  Nebraska. 


VI 


GENERAL  CONTENTS. 

PAGE. 

Preface '     .     v 

On  the  Equilibrium  of  Heat.    Pierre  Prevost    ....      1 
Treatise  on  Radiant  Heat  (Selections).    Pierre  Prevost  .        .     15 

Biographical  Sketch  of  Prevost 20 

An  account  of  some  Experiments  on  Radiant  Heat,    involv- 
ing an  extension  of  Prevost's  Theory  of  Exchanges. 

By  Balfour  Stewart 21 

Researches  on  Radiant  Heat.   Second  Series.    By  Balfour- 

Stewart .        .     51 

Biographical  Sketch  of  Stewart.        ...  .        .    72 

On  the  Relation  between  the  Emissive  and  the  Absorptive 
Power  of  Bodies  for  Heat  and  Light.    By  G.  R.  Kirch- 

hoff -73 

Biographical  Sketch  of  Kirchhoff        ...  .     97 

Chemical  Analysis  by  Spectral  Observations  by  G.  Kirch-  126 
hoff  and  R.  Bunsen    ...  ....     99 

Biographical  Sketch  of  Bunsen  .  .  126 

Bibliography 127 

Index    ,  .....  129 


Yll 


MEMOIR  ON  THE  EQUILIBRIUM  OF  HEAT. 

BY 

PIERRE  PREVOST. 

Journal  de  Physique,  vol.  38,  pp.  314-322.     Paris,  1791. 


CONTENTS. 


PAGE 

Outline  of  the  Proposed  Discussion 3 

Theory  of  the  Equilibrium  of  Heat     .....  4 

Rupture  of  the  Equilibrium  between  two  Portions  of  Space  6 

Phenomenon  of  Reflection  of  Cold       .        .        .        .        .  7 

Exclusion  of  an  Independent  Explanation  .         .         .         .  9 
Supplementary  Remarks  on  Radiant  Heat          .         .        .11 

Discussion  of  /Several  Discrete  Fluids         .     "  .  .     .         .  12 


MEMOIR  ON  THE  EQUILIBRIUM  OF  HEAT. 

BY  PIERRE  PREVOST. 

I  PROPOSE  to  analyse  and  fix  with  precision  the  sense  of  the 
word  equilibrium  applied  to  such  a  fluid  as  heat.  This  idea  is 
not  exactly  defined  in  the  theories  which  leave  questions  rela- 
tive to  the  nature  of  this  element  undecided.  If  there  is  any 
doubt  that  heat  is  material,  if  there  is  no  explanation  concern- 
ing the  contiguity  or  the  noncontiguity  of  molecules  of  heat, 
concerning  their  mobility  or  their  immobility,  the  kind  of 
motion,  vibratory  or  translatory,  which  is  attributed  to  them,  * 
it  is  impossible  to  arrive  at  exact  and  complete  ideas  of  their 
equilibrium.  It  results  from  this  that  every  phenomenon  which 
depends,  not  upon  any  equilibrium  whatever  but  upon  a  spe- 
cific kind  of  equilibrium,  remains  entirely  unexplained.  And 
as  the  imagination  determines  to  some  extent,  notwithstanding, 
that  which  reason  wishes  to  leave  undetermined,  the  true 
causes  are  lost  sight  of,  and  vain  hypotheses  are  arbitrarily 
preferred  because  they  are  suitable  in  certain  respects  and  fav- 
orable to  first  appearances. 

I  will  not  waste  time  in  discussing  the  different  natures 
assigned  to  heat  by  various  physicists.  The  true  constitution" 
of  this  fluid  is  connected  with  the  theory  of  discrete  fluids,  now 
known,  although  it  has  not  been  published  by  its  author.  For 
its  development  and  proof  I  refer  to  what  M.  DeLuc  has  said 
of  it  both  in  his  " Idees  sur  la  meteorologie"  and  in  his  letters 
published  successively  in  this  Journal:  also  what  I  have  said  of 
it  myself  in  my  essay  upon  I'origine  des  forces  magnetiques. 
Assuming  then  the  principles  of  this  theory,  I  shall  merely  recall 
them,  and  use  them  to  establish  true  ideas  on  the  equilibrium 
of  heat. 

I  shall  afterwards  make  the  application  of  this  theory  of  the 
equilibrium  of  heat  to  a  very  remarkable  phenomenon  which  I 
consider  inexplicable  without  it.  This  is  the  phenomenon  of 
the  reflection  of  cold.  It  has  been  observed  by  M.  Pictet,  who 

3 


MEMOIES    OK 

has  described  it  in  detail  in  his  essai  sur  le  feu.  This  learned 
scientist,  with  whom  I  have  old  and  valued  bonds  of  friendship, 
does  not  at  all  disapprove  of  the  discussion  which  I  am  under- 
taking although  it  tends  to  indicate  some  inadequacy  in  the 
explanation  which  he,  himself,  has  given  to  this  phenomenon. 
It  will  be  seen  elsewhere  by  what  I  shall  say  of  it,  that  a  com- 
plete explanation,  such  as  the  theory  of  M.  le  Sage  furnished, 
does  not  enter  into  the  plan  which  M.  Pictet  has  proposed.  I 
will  discuss  this  phenomenon  then, very  freely.  I  shall  show  that 
it  explains  itself  without  any  effort,  by  the  true  theory  of  dis- 
crete fluids.  I  shall  also  prove  that  it  is  not  explained  at  all  by 
the  imperfect  theories  to  which  physicists  commonly  limit 
themselves.  I  shall  close  this  memoir  with  two  remarks  which 
have  some  connection  with  this  subject,  without  being  directly 
related  to  it. 

I. 

THEORY   OF   THE    EQUILIBRIUM    OF   HEAT. 

Heat  is  a  discrete  fluid.     Its  elasticity  consists  in  its  expau- 
^   sive   force.     And   this   is  the   effect  of   the  movement  of   its 
particles.     This  movement  is  caused  by  the  impulse  of  a  much 
more  subtile  fluid  whose  effect  upon  its  particles  is  determined 
to  a  certain  extent  by  their  form.     It  is  so  swift  that  when  heat 
NO    is  freed  its  translation  from  one  place  to  another  appears  in- 
stantaneous.    It  is  also  sensibly  rectilinear,  so   that  perfectly 
free  heat  partakes,  as  far  as  the  movement  of  its  particles  is 
0  concerned,  of  all  the  properties  of  light,  at  least  so  far  as  our 
senses  can  determine  in  the  limited  experiments  which   have 
thus  far  been  performed. 

A  discrete  fluid  whose  particles  radiate  like  those  of  light, 
may  be  confined  by  barriers,  but  may  not  be  confined  by  an- 
other radiant  fluid  nor,  in  consequence,  by  itself.  For  it  is 
necessary  to  conceive  of  all  these  fluids  as  very  rare,  as  having 
many  more  void  intervals  than  full  ones  in  the  space  which 
they  occupy.  Light  does  not  stop  the  passage  of  light.  If  this 
solar  emanation  is  so  dense  that  two  luminous  currents  cannot 
cross  each  other  without  being  interrupted,  the  innumerable 
crossings  and  reflections  which  they  experience  will  destroy 
entirely  its  rectilinear  direction,  and  light  will  lose  to  our  eyes 

4 


RADIATION  AND   A  B  S  0  R  P  T  1 0  N . 

all  its  properties  which  depend  upon  this  direction.  What  is 
true  of  this  fluid  is  true  of  all  radiant  fluids.  Radiant  heat 
passes  through  heat,  which  upon  the  earth  is  present  in  all 
places,  and  since  it  produces  no  sensible  perturbation,  it  is  nec- 
essary that  these  particles  should  be  separated  by  intervals  great 
relatively  to  their  diameters.  It  is  certain  that  free  radiant 
heat  is  a  very  rare  fluid,  the  particles  of  which  almost  never 
collide  with  one  another  and  do  not  disturb  sensibly  their  mu- 
tual movements. 

In  conforming  to  physical  hypotheses,  one  says  ordinarily 
that  heat  is  coercible  by  itself  :  that  two  contiguous  portions  of 
heat  have  a  mutual  relation  when  their  temperatures  are  equal 
(or  as  M.  Volta  has  said,  when  their  tensions  are  the  same). 
These  expressions  are  exact,  only  in  so  far  as  they  define  an  ap- 
pearance. In  reality  the  heat  of  any  portion  cannot  arrest  that 
of  another.  These  two  heats  give  each  other  mutually  free 
passage.  It  would  then  be  wrong  for  one  to  conclude  from 
these  expressions  that  two  portions  of  contiguous  heat  restrain 
each  other  mutually,  as  two  bent  springs  stayed  against 
one  another,  or  as  two  masses  of  hair  which  repel  each  other 
by  their  elasticity. 

But  in  what  does  the  equilibrium  of  these  two  portions  of 
contiguous  heat  consist  ?  In  order  to  answer  this  question 
clearly,  I  will  suppose  the  two  portions  to  be  enclosed  in  an 
empty  space,  terminated  on  all  sides  by  impenetrable  walls. 
One  may  represent  two  cubes  applied  by  one  of  their  faces, 
forming  in  consequence  a  rectangular  parallelepiped  perfectly 
hollow,  of  which  the  six  faces  are  of  the  same  matter,  absolutely 
solid  and  without  pores.  The  two  portions  which  I  consider 
are,  in  this  example,  the  two  applied  cubes.  The  heat  occupy- 
ing the  interior  of  this  space  moves  freely  there,  and  as- 
suredly one  can  see  no  reason  why  it  should  pass  with  less 
facility  across  the  boundary  of  the  two  portions  than  across 
every  other  section  of  this  space.  There  are  then  continual  ex- 
changes from  one  portion  to  another,  and  one  can  affirm  (in 
consideration  of  the  number  of  particles  and  their  continual 
motion)  that  at  each  observable  instant  the  state  and  quantity 
of  the  heat  in  each  portion  are  constant.  There  is  then  no 
ceasing  of  the  different  particles,  which  are  found  at  any  one 

5 


MEM OIKS    ON 

place,  but  their  number  and  their  meau  distance  in  each 
portion  are  constant.  Concerning  their  speed,  as  it  is  in  the 
same  free  fluid  (consider  the  constant  nature  of  the  cause 
which  produces  and  renews  it  continually),  it  is  clear  that  it 
does  not  change  :  and  I  shall  leave  it  out  of  the  question,  since 
at  the  present  moment  I  consider  only  free  radiant  heat. 

At  all  times  that  both  portions  of  the  space  are  found  in  the 
circumstances  which  I  have  just  described,  the  heat  between 
them  is  in  a  state  of  equilibrium.  This  signifies  that  the 
phenomena  which  manifest  their  existence  remain  the  same  : 
that  if  these  phenomena  change  in  the  same  manner  and  in  the 
same  quantity  in  the  two  portions,  the  equilibrium  in  question 
will  not  be  disturbed.  This  would  occur  if  one  should  remove 
from  the  total  space,  which  we  are  considering,  a  certain 
aliquot  part  of  all  the  heat  found  there,  or  indeed  if  this 
aliquot  part  should  be  added.  The  identity  of  the  phenomena 
which  implies  the  equilibrium  of  heat  between  these  two  por- 
tions of  space  is  a  relative  identity,  which,  as  one  can  see,  may 
exist  whatever  may  be  the  difference  or  the  absolute  in- 
equality. 

Let  us  now  suppose  that  into  one  of  the  two  portions  of  space 
(which  I  will  represent  constantly  by  the  two  adjoining  cubes) 
one  passes  suddenly  some  new  heat ;  for  example,  one  tenth  of 
all  that  which  is  contained  in  this  portion.  This  heat,  in- 
stantly placed  in  motion,  spreads  immediately  throughout  all 
the  space  where  it  can  penetrate  freely.  Thus  the  exchanges 
between  the  two  portions  would  be  unequal.  One  would  send  to 
the  other  eleven  particles,  while  the  latter  would  return  only 
ten.  This  state  causes  a  rupture  of  the  equilibrium  between 
the  two  portions. 

By  reason  of  the  unequal  exchanges  one  may  conceive  that 
the  equality  would  be  reestablished.  Thus  the  rupture  of  the 
equilibrium  restores  very  quickly  the  equilibrium  between  two 
portions  of  free  heat.1 

1  Suppose  that  the  densities  of  the  heat  in  our  two  cubes  are  as  the 
numbers  1  and  2  (i.  e.,  that  one  is  twice  as  hot  as  the  other)  :  suppose 
further  that  in  one  second  there  passes  from  the  one  cube  to  the  other  a 
number  of  igneous  particles  which  on  the  whole  are  as  1  to  10  (so  that 
during  this  short  time  there  is  exchanged  one  tenth  of  all  the  heat). 

6 


RADIATION   AND   ABSORPTION. 

Absolute  equilibrium  of  free  heat  is  the  state  of  this  fluid  in 
a  portion  of  space  which  receives  as  much  as  it  allows  to 
escape  it. 

Relative  equilibrium  of  free  heat  is  the  state  of  this  fluid  in 
two  portions  oi'  space  which  receive  from  each  other  equal 
quantities  of  heat,  and  which  are,  moreover,  in  absolute  equilib- 
rium, or  experience  changes  precisely  equal. 

The  heat  of  several  portions  of  space  at  the  same  temperature 
and  near  each  other  is  at  once  in  the  two  kinds  of  equilibrium. 
If  one  should  change  the  temperature  of  all  the  space  at  the 
same  time,  it  would  destroy  the  absolute  equilibrium,  but  not 
the  relative  equilibrium.  Should  the  temperature  of  one  or 
of  several  portions  be  altered  without  affecting  all,  each  kind 
of  equilibrium  would  be  destroyed. 

If  the  cause  which  throws  out  or  which  absorbs  the  heat  of 
any  portion  is  an  instantaneous  cause,  after  the  action  of  this 
cause  the  relative  equilibrium  reestablishes  itself  incessantly 
by  means  of  unequal  exchanges.  And  after  this  reestablish- 
ment  the  absolute  equilibrium  remains  destroyed,  that  is  to 
say,  the  temperature  of  the  place  is  changed. 

If,  on  the  contrary,  the  cause  is  permanent,  that  is  to  say,  if 
there  is  opened  in  any  one  of  the  portions  of  this  space  a  source 
or  a  sink  which  gives  out  or  which  absorbs  heat  incessantly,  rela- 
tive equilibrium  tends  to  establish  itself,  but  does  not  reestablish 
itself  entirely  during  the  action  of  the  cause,  and  absolute 
equilibrium  is  constantly  destroyed. 

II. 

APPLICATION   OF   THE   PRECEDING   THEORY   TO   THE 
PHENOMENON    OF    REFLECTION  OF    COLD. 

Let  us  represent  two  spherical  concave  mirrors  opposite  to 
each  other  on  their  axes,  and  let  us  suppose  placed  at  their  foci 

After  seven  seconds  the  ratio  of  the  densities  of  the  heat  in  the  two 
cubes  will  be  as  5  to  6.  After  fourteen  seconds,  these  densities  will  be 
as  28  to  29,  i.  e.,  very  nearly  equality  :  the  equilibrium  will  appear 
established. 

I  take  this  result  from  a  calculation  of  M.  le  Sage  thirty  years  since  in 
the  case  of  discrete  fluids  different  from  heat. 

7 


MEMOIRS    ON 

two  bodies  precisely  equal  and  similar  and  of  the  same  sub- 
stance, which  JL  will  call  the  two  focal  bodies. 

To  simplify  this  I  will  suppose,  (1)  that  all  the  space  where 
the  apparatus  is  immersed  is  absolutely  cold  and  receives  heat 
only  from  part  of  the  two  focal  bodies,  (2)  that  these  are  hot 
and  give  out  radiant  heat  continuously,  (3)  that  the  mirrors  re- 
flect the  heat  but  do  not  absorb  it. 

With  these  conditions,  it  is  clear  that  the  heat  thrown  out  by 
either  one  of  the  two  focal  bodies  radiates  on  all  sides.  But  I 
shall  consider  only  the  part  which  strikes  the  mirror  of  which 
it  is  the  focus. 

This  heat  is  reflected  parallel  to  the  axis.  Striking  the  op- 
posite mirror  in  this  direction,  it  is  reflected  to  the  focus  of 
this  second  mirror  and  enters  as  a  consequence  the  body  which 
occupies  this  focus.  Similarly  inversely,  the  heat  thrown  out 
by  this  latter  against  its  mirror  enters  after  two  reflections  the 
body  which  occupies  the  focus  of  the  first  mirror. 

Let  us  suppose,  first,  the  two  focal  bodies  are  at  the  same 
temperature,  or  each  one  sending  out  in  equal  intervals  of  time 
an  equal  quantity  of  radiant  heat  to  its  own  mirror.  The 
relative  equilibrium  of  heat  between  the  two  focal  bodies  will 
not  be  disturbed  by  this  operation, ;  for  each  of  them  will  re- 
ceive from  the  other  exactly  what  it  gives  up  to  it.  Radiation 
will  exactly  compensate  absorption. 

Now  let  us  change,  to  a  greater  or  less  degree,  the  tempera- 
ture of  one  of  the  two  focal  bodies  ;  the  exchanges  made  between 
them  by  means  of  double  reflection  will  cease  to  be  equal :  the 
relative  equilibrium  will  be  destroyed.  It  will  tend  then  to  re- 
establish itself,  and  the  temperature  of  these  two  bodies  will  ap- 
proach each  other.  If  additional  heat  should  be  thrown  upon 
the  first  body,  for  example,  a  tenth  of  all  that  which  it  has,  the 
second  body  will  make  advantageous  exchanges  with  it.  For 
ten  particles  transmitted  by  reflection,  it  will  receive  eleven  by 
the  same  means  :  in  this  way  its  heat  will  be  augmented. 

If  one  should  withdraw  heat  from  the  first  body,  for  example 
a  tenth,  the-  second  body  will  make  exchanges  at  a  loss,  receiving 
nine  against  ten  by  means  of  the  mirror.  It  will  be  cooled. 

Such  is  the  result  of  the  theory  conforming  exactly  to  that 
of  the  ingenious  experiments  of  M.  Pictet,  in  spite  of  all  the 

8 


RADIATION   AND   ABSORPTION. 

conditions  which  1  have  made,  since  these  conditions  influence 
only  the  quantity  of  cold  or  of  heat  produced  by  reflection, 
and  not  the  nature  of  these  actions.  It  is  known  that  this 
physicist  has  observed  heat  and  cold  equally  reflected  in  his  ap- 
paratus, which  is  such  as  I  have  just  described.  He  has  not 
hesitated  to  explain  the  reflection  of  cold  just  as  that  of  heat  in 
a  reciprocal  sense :  but  being  limited  (conformably  to  his 
representation)  to  explanations  drawn  at  once  from  experiment, 
and  it  not  being  his  purpose,  in  the  important  work  which  he 
has  published,  to  treat  of  the  constitution  of  discrete  fluids,  he 
has  not  been  able  to  enter  into  the  details  which  I  have  just 
given.  It  has  resulted  from  this  that  the  view  to  which  he  has 
come  touching  the  cause  of  the  reflection  of  cold,  founded  upon 
these  notions  of  equilibrium,  inapplicable  to  discrete  fluids,  is 
insufficient  for  the  theory,  however  true  as  to  appearances. 

It  is  certain  that  when  one  produces  cold  at  the  focus  of  one 
of  the  mirrors,  the  heat  of  the  thermometer  placed  at  the  op- 
posite focus  follows  the  course  which  M.  Pictet  traces  for  it. 
And  this  course  is  what  I  have  just  described.  But  what  it  is 
that  causes  the  excess  heat  of  the  thermometer  to  take  this 
course,  this  physicist  has  not  shown  me,  because  he  has  not 
been  called  upon  to  consider  heat  according  to  its  natural  con- 
stitution. Now  if  one  holds  to  the  ideas  of  tension,  of  stress, 
in  a  word,  of  unvariable  equilibrium,  he  finds  that  the  progress 
of  the  phenomenon  of  heat  in  the  experiment  of  the  reflection 
of  cold  remains  absolutely  inexplicable.  I  shall  now  show,  (1) 
that  in  this  hypothesis  of  unvarying  equilibrium  no  heat  ought 
to  pass  from  the  thermometer  to  its  mirror,  (2)  that  if  any  does 
pass,  this  heat  should  not  converge  to  the  focus  of  the  other 
mirror. 


III. 

EXCLUSION  OF  THE  INDEPENDENT  EXPLANATION 
OF  THIS  THEORY. 

(I)  At  the  instant  when  one  places  a  cold  body,  such  as  glass, 
at  the  focus  of  one  of  the  mirrors,  the  heat  of  all  the  neighbor- 
ing bodies  passes  into  it.     This  cause  acts  according  to  the  law 
B  9 


MEMOIRS    ON 

of  the  inverse   square  of  the  distance,  when  we  suppose  the 
bodies  to  be  of  the  same  nature,  as  we  do  in  this  instance. 

The  mirrors  employed  in  the  experiment  of  the  reflection  of 
cold  were  placed  ten  and  one  half  feet  apart.  Their  curvature 
was  that  of  a  sphere  with  a  radius  of  nine  inches  :  so  that  their 
foci  were  about  four  and  one  half  inches  from  their  surface, 
measured  on  the  axis. 

If,  then,  we  consider  only  the  apparatus  without  taking  into 
account  the  supports,  or  the  air  or  the  surrounding  and  neigh- 
boring bodies,  it  is  clear  that  the  mirror  whose  focus  is  occu- 
pied by  the  glass,  being  twenty-eight  times  nearer  this  cold 
body  than  the  other  mirror,  ought  to  send  out  to  it  seven  him-, 
dred  and  eighty-four  times  as  much  heat  in  the  same  time. 

Further,  the  thermometer  placed  at  the  focus  of  this  other 
mirror  being  nearer  the  glass  than  its  mirror  in  the  ratio  of  26 
to  27,  ought  to  set  free  more  heat  than  a  portion  of  the  mirror 
equal  to  its  bulb  in  the  double  inverse  ratio  (at  least  for  the 
part  of  the  mirror  which  lies  at  the  origin  of  the  axis).  This 
ratio  is  that  of  729  to  676,  or  of  about  13  to  12  ;  so  that, 
through  the  direct  influence  of  the  glass,  the  thermometer  loses 
about  a  thirteenth  more  of  its  heat  than  if  it  formed  a  part  of 
the  mirror,  at  the  focus  of  which  it  is  placed.  When  the  cool- 
ing of  the  first  mirror  becomes  sensibly  equal  to  the  second,  the 
thermometer  being  less  distant  than  the  former,  is  also  more 
affected  by  the  latter  in  the  double  inverse  ratio  of  27  to  28  ; 
that  is  to  say,  in  the  ratio  of  784  to  729,  or  of  about  14  to  13. 

Thus  the  thermometer  is  cooled  more  than  its  mirror,  either 
directly  by  the  glass,  or  indirectly  by  the  mirror  whose  focus 
this  glass  occupies.  Heat  here  then  is  under  less  tension  than 
in  the  mirror.  Consequently  it  cannot  pass  from  the  thermome- 
ter to  the  mirror,  nor  in  consequence,  radiate  from  there  to  the 
opposite  mirror  next  the  glass.  This  progress  of  the  phenomena 
in  a  system  in  unvarying  equilibrium  is  contrary  to  the  effect 
which  the  cause  should  occasion.  And  it  is  still  more  inexpli- 
cable when  we  consider  the  supports  of  the  apparatus  and  all 
the  surrounding  bodies  which  send  heat  into  the  glass,  and 
constantly  draw  out  that  of  the  thermometer,  as  well  as  of  the 
opposite  mirror:  effects  independent  of  reflection  and  of  the 
particular  position  of  the  foci. 

10 


RADIATION  AND  ABSORPTION. 

(II).  To  which  it  is  necessary  to  add,  in  reconciling  the 
same  (which  is  demonstrated  false  in  the  hypothesis  I  have  dis- 
cussed), that  the  heat  of  the  thermometer  passes  in  part  into 
its  mirror;  as  there  is  carried  over  only  what  replaces  that  which 
escapes,  this  heat  would  not  be  reflected,  but  absorbed.  Now, 
all  the  heat  which  one  of  the  mirrors  sends  out  to  the  other, 
aside  from  that  by  reflection  to  the  focus,  being  an  irregular 
radiation,  would  not  converge  at  the  focus  of  the  other  mirror. 
THUS  the  foci  would  not  be  more  characteristic  than  two  other 
points,  taken  at  random  between  the  mirrors,  for  repeating  the 
experiment  of  reflection  of  cold,  which  is  absolutely  contrary 
to  the  actual  observation. 

It  is  apparent,  then,  that  if  we  refuse  to  consider  heat 
according  to  its  true  constitution  as  a  discrete  fluid,  whose 
particles  are  in  motion,  and  if  in  consequence  we  do  not  arrive 
at  ideas  which  I  have  given  of  the  equilibrium  of  radiant  free 
heat,  it  is  impossible  to  give  any  satisfactory  explanation  (com- 
patible moreover  with  the  principles  of  sound  physics),  of  this 
beautiful  and  remarkable  phenomenon  of  the  reflection  of  cold. 
The  fact  is  established  by  an  excellent  observer,  who  has  very 
clearly  recognized  the  progress  of  the  phenomena  of  heat.  The 
discovery  of  the  cause  is  due  to  the  author  of  the  true  theory  of 
discrete  fluids. 


IV. 


SUPPLEMENTARY  REMARKS. 

(1).  Radiant  heat  is  only  a  part  of  the  heat  that  escapes  from 
a  hot  body.  Let  us  suppose  that  in  the  preceding  experiment 
the  two  foci  of  the  mirrors  communicate  by  a  metallic  bar,  termi- 
nated at  both  ends  by  these  foci:  if  we  place  at  one  end  of  the 
extremities  of  this  bar  an  exhaustless  source  of  heat  (a  red-hot 
iron,  a  blast-lamp  flame,  the  focus  of  a  powerful  lens):  immedi- 
ately the  radiant  heat,  following  the  course  indicated  above, 
will  warm  the  other  extremity  of  the  bar  by  the  double  reflec- 
tion. At  the  same  time  the  non-radiant  heat,  creeping  gradu- 


MEMOIKJ3     ON 

ally  into  the  contiguous  parts  of  the  bar,  will  slowly  heat  it  and 
will  finally  come  to  the  points  most  distant  from  the  source. 

The  air  being  a  discrete  fluid  much  more  dense1  than  heat, 
arrests  and  intercepts  the  particles  of  the  latter.  But  being 
much  more  rare  than  the  metal,  it  allows  a  portion  of  it  to  pass, 
which  produces  the  phenomena  of  radiant  heat.  Light,  much 
more  rare  and  subtle  than  heat,  is  transmitted  in  much  greater 
proportion  by  this  same  air,  the  opacity  of  which  is  so  incon- 
siderable that  it  becomes  sensible  only  in  very  great  masses.2 
The  transparency  or  the  quantity  of  fluid  transmitted  through 
another  fluid,  depends  upon  the  rarity  and  the  subtlety  of  the 
particles  of  both  fluids.  I  do  not  speak  here  of  the  affinities 
and  capacities  of  different  bodies  for  heat.  I  speak  only  of  the 
mechanical  interception  of  this  fluid  by  its  solid  parts.  This 
interception  is  sufficient  only  to  produce  these  two  kinds  of 
heat  or  of  cold,  radiant  heat,  and  nonradiant  heat. 

Entangled,  further,  in  the  small  cavities  or  in  the  interstices 
of  solid  particles,  the  heat  may  or  may  not  recover  all  the  veloc- 
ity which  properly  belongs  to  it,  according  as  these  cavities  or 
interstices  are  or  are  not  sufficiently  spacious.  When  it  recov- 
ers only  a  portion  of  its  velocity,  it  becomes  in  part  insensible 
or  latent.  When  it  can  recover  only  a  very  little  of  it  or  none 
at  all,  it  yields  to  the  affinities  of  the  particles  which  surround 
it  and  combines  in  a  thousand  ways. 

(2).  Heat  is  not  the  only  fluid  of  its  kind.  Several  discrete 
fluids  are  known,  radiant  and  nonradiant.3  We  often  have 
occasion  to  consider  these  fluids  in  the  state  of  equilibrium. 
The  determination  of  the  true  sense  of  this  word  ought  then  to 
be  of  much  importance,  independently  of  the  theory  of  heat. 


1  The  density  which  I  attribute  to  the  air  in  this  instance,  consists 
chiefly  in  the  proximity  of  its   molecules;  for  a  discrete  fluid  maybe 
composed  of  very  dense  particles,  but  with  large  spaces  between  them : 
so  that  it  could  be  more  permeable  than  heat,  although  more  dense. 

2  Notice  the  remarks  of  M.  de  Saussure,  upon  the  transparency  of 
the  air,  in  his  memoirs  upon  light.     Academ.  de  Turin,  1790. 

8  In  the  electrical  phenomena,  there  are  radiations  of  the  correspond- 
ing fluid.  In  magnetic  phenomena  neither  of  the  two  magnetic  fluids  is 
radiant. 

12 


RADIATION    AND    ABSORPTION. 

If  these  remarks  and  the  preceding  discussion  offer  any 
useful  views,  if  they  tend  to  throw  light  upon  an  important 
class  of  phenomena,  if  they  suggest  any  clear  ideas  upon  the 
method  of  motion  of  invisible  and  subtle  fluids  which  manifest 
their  existence  by  such  diverse  appearances  :  finally,  if  these 
conceptions  naturally  connect  themselves  with  other  theories, 
either  already  proven,  or  rendered  probable,  concerning  the 
various  effects  of  these  subtle  fluids  (such,  as  the  phenomena  of 
evaporation,  of  electricity  and  of  magnetism),  is  it  not  the 
requital  of  investigating  the  general  theory  upon  which  all 
these  special  explanations  depend  ?  This  theory  (I  refer  to 
that  of  M.  le  Sage  of  Geneva,  upon  the  nature  of  discrete 
fluids)  merits  the  further  attention  of  physicists,  since  it  depends, 
itself,  upon  another  principle,  more  general,  which  has  also  as 
a  proof  of  its  reliability,  the  clear  and  satisfactory  explanation 
of  very  striking  and  very  general  phenomena,  absolutely  in- 
explicable without  it. 


13 


ON  RADIANT  HEAT. 

BY 

PIERRE  PREVOST. 

Geneva,  1809. 
(Selections.) 


15 


CONTENTS. 


PAGE 

Questions  Relative  to  the  Nature  of  Caloric          .     _  .         .      17 
Resume  of  Principles  and  Conclusions.        .        .         .         .      19 


16 


QUESTIONS  RELATIVE  TO  THE  NATURE 
OF  CALORIC. 

CHAPTER  IV.    PP.  6 — 10. 

THE  word  caloric  (heat)  has  been  originated  to  explain  the 
cause  of  heat,  with  the  formally  expressed  intention  of  being 
non-committal  as  to  its  nature. 

It  is  desirable  to  leave  it  indefinite  as  to  whether  heat  may  be 
produced  by  a  specific  fluid,  or,  merely,  be  a  movement 
impressed  upon  the  molecules  of  a  body,  without  the  introduc- 
tion of  any  fluid. 

Many  noted  physicists  believe  there  is  no  specific  fluid  to 
which  this  word  caloric  is  applicable.  They  believe  that  heat 
is  produced  by  internal  movements  of  the  molecules  of  a  body. 
More  often,  however,  physicists  have  recourse  to  a  vibrating 
ether  or  to  the  air,  or  to  some  other  medium  propagating  waves 
to  which  they  attribute  the  phenomena  of  heat. 

Others  believe  that  caloric  is  a  specific  fluid,  which  penetrates 
the  body  and  produces  all  the  appearances  of  this  kind. 

Among  the  latter,  many  believe  that  caloric  and  light  are 
identical.  Others  are  of  a  contrary  opinion. 

Some  look  upon  caloric  as  simple  ;  a  smaller  number  regard  it 
as  a  compound  fluid.  Mr.  J.  A.  DeLuc  believes  that  caloricis,  a 
kind  of  vapor  composed  of  ponderable  matter  held  in  a  state  of 
suspension  by  light.  This  conception  throws  some  light  upon 
many  phenomena  and  merits  serious  consideration.  Meanwhile, 
pressed  to  arrive  at  the  chief  object  which  I  have  in  view,  I 
will  refrain  from  all  discussion  as  to  the  composition  of  caloric. 

I  have  no  desire  to  repeat  here  and  weigh  the  general 
arguments  stated  on  the  one  side  and  on  the  other  for  sus- 
taining the  various  views  which  I  have  just  outlined.  I  will 
limit  myself  to  a  very  few  remarks  on  this  subject. 

As  stated  below  I  propose  to  consider  caloric  as  a  specific 
fluid.  I  will  represent  the  radiations  of  this  fluid  as  an  emission 

17 


RADIATION    AND    ABSOKPTION. 

and  never  as  an  undulation.  I  believe  this  conception  and  this 
representation  to  be  more  conformable  than  any  other  to  the 
nature  of  things  and  founded  upon  the  soundest  principles  of 
general  physics.  But  if  those  who  believe  otherwise  substitute 
waves  for  an  emission  they  may  be  able,  perhaps,  to  adapt  to 
their  opinion  the  explanations  which  I  give  for  phenomena  of 
this  crass.  It  is  no  desire  of  mine  that  they  should  attempt  it, 
because  I  am  persuaded  that  this  would  be  translating  a 
language  clear  and  natural  into  a  language  obscure  and  artificial. 
But  I  make  this  statement  to  make  clear  the  kind  of  work 
which  I  have  undertaken.  I  do  not  contest  any  system.  I  do 
not  refute  any  explanation.  It  is  my  aim,  in  limiting  myself  in 
my  subject,  to  explain  in  my  own  way  what  seems  to  me  to  ad- 
mit of  clear  explanation,  and  to  indicate  the  phenomena  of 
which  the  explanation  remains  imperfect.  If  each  one  who 
has  an  opinion  upon  the  theory  of  caloric  will  give  a  concise  ex- 
position of  his  ideas  on  the  subject,  and  will  show  how  the  facts 
may  be  coordinated  by  means  of  these  conceptions  :  physicists 
can  see  at  a  glance  which  theory  is  most  satisfactory,  or  if  all 
should  be  rejected. 

RESUME  OF  THE   PRINCIPLES   EXPOUNDED   AND   OF   THE   PRINCI- 
PAL CONCLUSIONS   WHICH    HAVE    BEEN    DEDUCED 
FROM   THEM. 

SECTION  IX.  pp.  258—261. 

HEAT  is  a  discrete  fluid;  each  element  of  heat  follows  con- 
stantly the  same  straight  line,  as  long  as  no  obstacle  arrests  it. 
Every  point  of  a  hot  space  is  constantly  traversed  throughout 
by  streams  of  heat. 

If  we  admit  this  constitution  of  heat,  the  following  conclu- 
sions are  inevitable. 

The  first  three  require  nothing  further.  The  others  require 
the  assumption  that  heat  is  comparable  with  light  in  its  move- 
ments of  reflection  and  refraction. 

1st.  conclusion:  Free  heat  is  a  radiant  fluid.  Or,  as  the 
surface  of  the  body  of  heat  becomes  free,  each  point  of  the  sur- 

18 


MEM01KS    ON 

face  of  the  body  is  a  center  to  which  tend,  and  from  which  are 
carried,  in  every  direction,  streams  of  heat. 

2nd.  conclusion :  The  equilibrium  of  heat  between  two 
neighboring  free  spaces  consists  in  the  equality  of  the 
exchanges. 

3rd.  conclusion:  When  the  equilibrium  is  disturbed,  it  is 
reestablished  by  unequal  exchanges,  in  a  medium  of  constant 
temperature,  a  body  that  is  hotter  or  colder  requires  this  tem- 
perature according  to  the  law  that  the  periods  of  time  being  in 
arithmetical  progression,  the  differences  of  temperature  are  in 
geometrical  progression. 

4th.  conclusion:  In  a  space  of  uniform  temperatures,  if  a 
reflecting  or  refracting  surface  is  introduced  it  has  no  effect  in 
changing  the  temperature  of  any  part  of  this  space. 

5th.  conclusion:  In  a  space  of  unequal  temperature,  if  there 
is  placed  a  body  which  is  either  hotter  or  colder  and  if  after- 
wards a  reflecting  or  refracting  surface  be  introduced,  the 
points,  upon  which  these  surfaces  direct  the  rays  emanating 
from  this  body,  will  be  affected  by  it,  being  heated  if  the 
body  is  hotter,  or  cooled  if  it  is  colder. 

6th.  conclusion:  A  reflecting  body,  having  been  heated  or 
cooled  internally,  recovers  the  surrounding  temperature  more 
slowly  than  a  nonreflector. 

7th.  conclusion:  A  reflecting  body,  having  been  heated  or 
cooled  internally  will  have  less  effect  on  another  body  placed 
at  any  distance  (in  heating  or  cooling  it)  than  a  nonreflector 
would  under  the  same  conditions. 

All  these  conclusions  have  been  verified  experimentally,  ex- 
cept that  concerning  the  refraction  of  cold.  This  experiment 
remains  to  be  made,  and  I  am  confident  of  the  result,  at  least 
if  the  refraction  of  the  heat  is  capable  of  being  observed.  This 
result  is  indicated  in  the  4th.  and  5th.  conclusions,  which  could 
in  this  way  be  submitted  to  a  new  test.  It  is  hardly  necessary 
to  indicate  in  this  place  the  precautions  by  means  of  which  one 
would  place  himself  beyond  every  kind  of  misobservation. 


19 


RADIATION    AND    ABSORPTION. 

BIOGRAPHICAL  SKETCH. 

PIERRE  PREVOST  was  born  in  Geneva,  March  3,  1751,  and  died 
at  the  same  place  oil  the  9th  of  April,  1839.  He  was  the  son  of 
a  clergyman  and  was  educated  for  a  clerical  career,  but  turned 
his  attention  to  law  and  later  to  educational  work.  He  became 
a  professor  of  philosophy  and  a  member  of  the  Academy  of 
Sciences  at  Berlin  in  1780.  Here,  through  his  acquaintance 
with  Lagrange,  his  attention  was  directed  to  science,  which 
later  he  followed  up  with  his  studies  on  Magnetism  and  Heat 
at  Geneva  where  he  became  professor  of  physics  in  1810.  He 
published  much  on  different  subjects,  including  philology, 
philosophy,  political  economy,  fine  arts,  etc.  He  issued  the 
works  of  le  Sage,  supplemented  by  many  additions  of  his 
own.  His  Du  Calorique  Rayonnant  appeared  at  Geneva  in 
1809  and  was  an  exposition  and  extension  of  his  theory  of  ex- 
changes first  advanced  several  years  before.  The  original 
memoir  and  later  publications  appeared  in  the  Journal  de 
Physique  and  the  Phil.  Trans,  from  1791  to  1802.  His  remark- 
able versatility  is  indicated  in  the  variety  of  his  publications. 
His  most  valuable  contribution  to  science  is  undoubtedly  his 
Theory  of  Exchanges  one  of  the  most  important  principles  in 
the  whole  range  of  physical  science. 


20 


AN    ACCOUNT    OF  SOME    EXPERIMENTS 

ON  RADIANT  HEAT,   INVOLVING  AN 

EXTENSION  OF  PREVOST'S  THEORY 

OF  EXCHANGES. 

BY 

BALFOUR  STEWART. 

Transactions  of  the  Royal  Society  of  Edinburgh. 
Vol.  XXII.  Part  I.  pp.  1—20.  March,  1858. 


CONTENTS. 


PAGE 

Division  of  Subject 23 

Description  of  Instruments  and  Method     .        .        .        .24 

On  Radiations  from  plates  of  Different  Substances     .         .  26 
On  Radiations  from  Polished  Surf  aces        .                 .         .32 

On  Radiations  of  Plates  of  Different  thicknesses        .         .  33 

Results  Explained  by  Prevost's  Ttieory  of  Exchanges .         .  35 
Peculiarities  of  the  Radiation  from  Plates  of  Diatherm- 

anous  Substances 37 

Equality  of  the  Radiation  and  the  Absorption     .  40 
Influence  of  the  Reflective  and  Refractive  Powers  of  Bod- 
ies on  their  Radiation  considered 42 

Equal  and  Independent  Radiation       .....  47 

Internal  Radiation  and  Conduction    ,  49 


22 


l.    AN  ACCOUNT  OF  SOME  EXPERIMENTS 
ON  RADIANT  HEAT,  INVOLVING 
AN  EXTENSION  OP  PEEVOST'S 
THEORY  OF  EXCHANGES. 

BY  BALFOUR  STEWART,  ESQ. 

COMMUNICATED  BY  PROFESSOR  FORBES. 

Read,  15th,  March  1858. 

Division  of  Subject. 

1.  This  paper  consists    of  two  parts,  the  first  of  which  is 
confined  to  describing  the  experiments    performed;    while  in 
the  second  it  is  attempted   to  connect  these  with  certain  theo- 
retical views  regarding  Radiant  Heat. 

2.  The  experiments  were  made    with  a  fourfold  object;  at 
least  for  the  sake  of  clearness,  it  is  well  to  class  them  into  four 
distinct  groups: — 

Group  L  Contains  those  experiments  in  which  the  quanti- 
ties of  heat  radiated  from  polished  plates  of  different 
substances,  at  a  given  temperature,  are  compared  with 
the  quantity  radiated  from  a  similar  surface  of  lamp- 
black, at  the  same  temperature. 

Group  II.  Those  in  which  the  quantities  of  heat  radiated 
at  the  same  temperature,  from  polished  plates  of  the  same 
substance,  but  of  different  thicknesses,  are  compared 
with  one  another. 

Group  III.  Those  in  which  the  radiations,  from  polished 
plates  of  different  substances  at  any  temperature,  are 
compared  with  that  from  lampblack  at  the  same  tem- 
perature, with  regard  to  the  quality  or  nature  of  the 
heat  radiated. 

23 


MEMOIRS     ON 

Group  IV.  Those  in  which  the  same  comparison  is  made 
between  the  radiations  from  polished  plates  of  the  same 
substance,  bu»t  of  different  thicknesses. 

Instruments  used,  and  Method  of  using  them. 

3.  I  am  indebted  to  the  kindness  of  Professor  Forbes  for 
the  use  of  a  delicate  thermo-multiplier,  consisting  of  the  sen- 
tient pile,  and  its  attached  galvanometer  and  telescope;  as 
well  as  for  much  valuable  information  with  regard  to  the 
proper  method  of  using  the  apparatus. 


The  following  arrangement  was  adopted  for  the  great  mass 
of  the  experiments: 

A.  Is  the  sentient  pile,  with  a  polished  brass  cone  attache^ 
to  it,  for  collecting  the  rays  of  heat. 

B.  Is  the  galvanometer,  the    position  of  its  needle   being 
read  to  ^th  of  a  degree  by  the  telescope  C. 

D.  Is  a  screen  placed  before  the  mouth  of  the  cone  in 
which  there  is  a  small  hole  or  diaphragm  .65  inch  square.  The 
screen  is  covered  with  gilt  paper,  in  order  that,  should  it  get 
slightly  heated,  it  might  radiate  as  little  as  possible. 

The  heated  body  is  placed  behind  the  diaphragm,  filling  up 
the  field  of  view  from  the  cone  ;  so  that  every  ray  reaching  the 
cone  from  behind  the  diaphragm  comes  from  the  heated  body. 

24 


RADIATION   AND   ABSORPTION. 

In  the  following  experiments,  unless  the  contrary  is  men- 
tioned, the  distance  of  the  diaphragm  from  the  mouth  of  the 
cone  is  2  inches. 

The  dimensions  of  the  cone  itself  are  as  follows  : 

Length  of  axis,  or  distance  between  centre  of  mouth  and 

pile, 5    inches. 

Diameter  of  mouth  or  opening, 2.6  inches. 

The  temperature  to  which  the  heated  body  was  raised  was 
generally  212°,  and  the  apparatus  used  for  heating  it  was  of  the 
following  construction  : 

It  consisted  of  a  tin  vessel,  having  its  top,  bottom,  and  sides 
double  (or  a  box  within  a  box),  and  furnished  on  the  top  with 
a  lid,  also  double,  by  means  of  which  the  body  to  be  heated  was 
introduced   into   the   interior. 
Water    was    poured   into   the 
chamber  between  the  outer  and 
inner    boxes,   and   allowed   to 
boil ;    and,  when   the  lid    was 
shut,  the  temperature  of   the 
interior  was  found  to  rise  very 
nearly  to  the  boiling  point  ;  a 
thermometer     placed     in    the 
air  of   the  chamber  showing  a 

temperature  of  200°,  and  when  lying  on  the  bottom, 
a  temperature  of  210°.  When  an  observation  was  to  be  made, 
the  hot  body  was  taken  out,  and  that  surface  which  lay  on  the 
bottom  of  the  inner  chamber  placed  behind  the  diaphragm,  so 
as  to  radiate  into  the  cone.  In  the  following  experiments,  un- 
less the  contrary  is  mentioned,  the  body  has  been  heated  in  this 
manner. 

The  first  swing  of  the  galvanometer  needle  was  taken  as  rep- 
resenting the  intensity  of  the  heating  effect  :  and  Professor 
Forbes  has  shown,  in  a  paper  read  before  this  Society,  2d  May, 
1836,  that  this  will  hold  up  to  angles  of  about  20°,  which  is  the 
maximum  deviation  used  in  these  experiments. 

Observations  were  always  made  with  as  little  sunlight  as  pos- 
sible ;  and  under  these  circumstances,  it  was  ascertained  that 
the  stray  heat  reaching  the  cone  was  inappreciable.  The  needle, 
it  was  calculated,  reached  the  limit  of  its  swing  about  12 

25 


MEMOIRS    ON 

seconds  after  the  heated  body  had  been  taken  out  of  the 
boiling-water  apparatus. 

Experiments  were  made  to  ascertain  if  the  body  cooled 
sensibly  during  this  short  period  of  time,  and  it  was  found  that 
its  cooling  was  so  trifling  as  not  to  interfere  in  any  degree  with 
the  results  of  these  observations.  In  the  following  experiments, 
it  is  therefore  assumed  that  the  body  remains  at  its  original 
temperature  of  210°  while  the  observation  is  being  made. 

Four  observations  were  generally  made,  and  three  if  they 
agreed  together  exceedingly  well,  but  never  fewer.  Very  often 
the  agreement  was  exact.  . 

First  Grout  of  Experiments  described. 

4.  With  these  remarks,  I  proceed  to  describe  the  experiments 
belonging  to  the  first  group,  or  those  made  with  the  view  of 
comparing  the  heat  radiated  from  polished  plates  of  different 
substances  with  that  radiated  from  a  surface  of  lampblack  at 
the  same  temperature. 

The  reason  why  lampblack  was  chosen  as  the  standard  is  ob- 
vious ;  for,  it  is  known  from  Leslie's  observations,  that  the 
radiating  power  -of  a  surface  is  proportional  to  its  absorbing 
power.  Lampblack,  which  absorbs  all  the  rays  that  fall  upon 
it,  and  therefore  possesses  the  greatest  possible  absorbing  power, 
will  possess  also  the  greatest  possible  radiating  power.  The  first 
substance  compared  with  it  was  glass. 

A.  Glass. — Apiece  of  plate  glass,  .3  inch  thick,  having  paper 
coated  with  lampblack  pasted  on  its  surface  next  the  pile,  gave 
a  deviation  of  18.1.  This  may  be  taken  as  the  radiation  from 
lampblack. 

Three  plates  of  crown  glass,  each  .05  inch  thick,  placed 

one  behind  the  other,  gave 17.7. 

A  single   piece   of  crown  glass  of   the  same  thickness, 
gave 16.5. 

This  difference  is  probably  owing  to  the  single  plate  cooling 
faster  than  the  three  plates.  It  may  be  argued  that  the 
radiation  from  the  glass  is  very  nearly  equal  to  that  from  lamp- 
black ;  and  indeed  this  is  already  well  known.* 

*  See  Leslie's  "  Inquiry  into  Nature  and  Propagation  of  Heat." 

26 


RADIATION   AND   ABSORPTION. 

B.  Alum. — Here  the  boiling- water  apparatus   could  not  be 
used,  since  alum   becomes   calcined   at   a   temperature   much 
below  212°  ;  but  a  self-regulating  apparatus,  invented  by   the 
late    Mr.    Kemp,    was    employed    instead,    giving    a    steady 
temperature  of  98°. 

A  piece  of  plate  glass  .18  inch  in  thickness,  gave 5.0 

A  piece  of  alum  of  the  same  thickness  gave 5.0 

The  radiation  from  the  alum  may  therefore  be  reckoned 
equal  to  that  from  glass. 

C.  Selenite. — At  the  temperature  of  98° — 

A  piece  of  selenite  .125  inch   in   thickness   gave. . .  .5.1 

Under    the   same  circumstances,  glass   .18   inch   thick 

gave 5.0 

In  the  boiling-water  apparatus, 

The  same  piece  of  selenite  gave 18.0 

While   blackened    glass    gave 18.5 

The  radiation  from  selenite  may  therefore  be  reckoned  equal 
to  that  of  alum  or  glass. 

D.  Mica. — A  small  box  was  constructed,  having  two  windows 
of  mica,  the  thickness  of  the  mica  in  the  one  being  .0009  inch, 
and  of   that  in  the   other. 02   inch.     This  box  was   filled  with 
mercury  (Professor   Forbes  having  suggested  the  use  of  that 
metal,  to  keep  up  the  temperature,  while  interfering  very  little 
with  the  radiation).     The  whole  was  then  set  on  a  glass  dish  in 
the  boil  ing- water  apparatus. 

The  radiation  from  the  thin  window  was   11.2 

While  that  from  the  thick  window  was 12.7 

As  it  would  have  been  manifestly  erroneous  to  compare  these 
with  the  radiation  from  the  blackened  glass  lying  in  contact 
with  the  bottom  of  the  apparatus,  the  thin  window  was 
removed,  and  the  blackened  paper  substituted  in  place  of  it. 

While  the  thick  mica  window  gave 12.7 

The  blackened  paper  gave 13.8 

In  comparing  the  radiations  from  the  two  windows,  they 
were  observed  alternately.  We  see,  therefore,  that  the  radia- 
tion from  mica,  especially  thin  mica,  is  less  than  from  lamp- 

27 


MEMOiKS     ON 

black  in  the  proportion  of  11.2  to  13.8,  or  the  heat  from  thin 
mica  is  80  per  cent  of  that  from  lampblack. 

E.  Rock  Salt. — As  in  the  experiments  with  rock  salt,  it  was 
desirable  to  obtain  results  of  the  greatest  possible  accuracy,  the 
radiation  from  rock  salt  was  not  compared  with  that  from 
blackened  glass  ;  for  it  was  found  that  glass  cooled  more 
rapidly  than  rock  salt. 

The  following  plan  was  adopted  : — 

A  piece  of  rock  salt  .18  inch  thick  (the  temperature  as 
in  all  the  previous  examples  being  about  210°,  gave  3.2 
A  canister  with  water  kept  boiling,  coated  with  lamp- 
black   22.0 

In  order  to  estimate  how  much  the  rock  salt  had  cooled 
during  the  observation,  the  following  experiment  was  made, 
without  any  diaphragm  : — 

Rock  salt  .18  inch  thick  taken  to   the   cone   at   once, 

gave 5.1 

After  cooling  for  15  seconds,  it  gave 4.9 

It  will  be  seen  from  this,  that  were  the  rock  salt,  instead  of 
cooling  during  the  12  seconds  necessary  for  the  observation, 
kept  at  the  temperature  of  212°  ,  it  would  not  have  given  more 
than  3.3,  while  the  hot-water  canister  gave  22.0. 

5.  From  these  experiments,  it  appears  that  glass,  alum,  and 
selenite,  at  low  temperatures,  have  an  intensity  of  radiation 
very  nearly  equal  to  that  from  lampblack  ;  while  mica  radiates 
somewhat  less,  and  rock  salt  greatly  less.  This  is  shown  by 
the  following  table  : 


TABLE  I. 


RADIATING  SUBSTANCE. 

TEMPERATURE. 

212° 

98° 

Lampblack,  >  

100 

98 

98 
92 
81 
15 

27 

27 
27 

Glass 

Alum 

Selenite,  

Thick  mica,  

Thin  mica,  

Rock  salt 

28 


RADIATION   AND    ABSORPTION. 

Second  Group  of  Experiments  described. 

6.  I  now  proceed  to  the  second  group  of  experiments,  or  those 
designed  to  compare  together  the  quantities  of  heat  radiated 
at  the  same  temperature  from  polished  plates  of  the  same  sub- 
stance, but  of  different  thicknesses. 

A.  Glass. — No  direct  experiment  of  this  kind  was  made  on 
glass  ;  for  although  a  thick  plate  gave  a  somewhat  greater 
radiation  than  a  thin  plate,  it  was  imagined  that  this  was  due 
to  the  unequal  cooling  of  the  two  plates.  Indirectly,  however, 
we  may  gather  that  thick  glass  radiates  somewhat  more  than 
thin  glass,  from  the  following  experiment,  which  belongs  more 
properly  to  the  fourth  group: 

A  plate  of  crown  glass  .05  inch  thick,  being  placed  be- 
fore the  cone  as  a  screen,  and  a  similar  plate  .05  inch 
thick,  and  3.75  inches  square,  being  used  as  the 
source  of  heat  at  a  distance  of  6  inches,  and  no  dia- 
phragm used,  the  deviation  was  0.95* 

But  when  the  source  of  heat  was  a  similar  plate  .10 
inch  thick,  the  deviation  became  1.45 

Such  a  difference  cannot  be  accounted  for  by  the  unequal 
cooling  of  the  plates  ;  and  it  would  seem  to  indicate  that  a  small 
quantity  of  heat  from  the  interior  of  the  thick  plate  reached 
the  surface  ;  which  heat,  having  already  been  sifted  by.  its  pas- 
sage through  glass,  was  easily  able  to  pierce  the  screen. 

In  another  similar  experiment, 

One  piece  of  crown  glass  .05  inch  thick,  gave  a  deviation 

of 1.1 

Two  plates  .05  inch  thick,  the  one  behind  the  other,  1.55 
Three  such  plates, 1.9 

B.  and  C. — No  experiments  of  this  kind  were  attempted  with 
alum  or  selenite. 

D.  Mica. — Experiments  similar  to  those  already  described, 
only  at  a  distance  of  2^  inches  from  the  cone,  gave — 


*  Without  any  screen,  it  was  calculated  that  the  intensity  of  effect 
would  have  been  equal  to  about  150°. 


MEMOIRS    ON 

For  mica  .0009  inch  thick  (average  of  two  sets  of  experi- 
men  ts), 8.2 

For  mica,  .02  inch  thick  (average  of  two  sets  of  experi- 
ments),    .9.3 

The  experiments  already  quoted,  which  were  made  at  a 
shorter  distance  from  the  pile,  gave — 

For  mica,  .0009  inch  thick, 11.2 

For  mica,  .02  inch  thick, 12.7 

E.  Rock  Salt. — Three  pieces  of  rock  salt  were  used.  Their 
dimensions  were: 

1st  Piece.  2nd  Piece.  3rd  Piece. 

Length 1.15  inch  2.15  inches  2.5  inches 

Breadth 1.15     "  1.4   inch  1.4  inch 

Thickness... .0.18     "  0.36    "  0.77  " 

For  these  pieces,  as  well  as  for  the  other  substances,  I  am  in- 
debted to  the  kindness  of  Professor  Forbes.  When  placed  be- 
hind the  diaphragm,  the  farthest  off  surface  was  large  enough 
to  fill  up  the  field  of  view, — that  is  to  say,  all  rays  from  the 
cone  striking  the  nearest  surface  struck  also  the  surface  far- 
thest off  ;  the  distance  between  the  two  surfaces  being  the 
thickness  of  the  piece. 

The  following  are  the  means  of  four  sets  of  experiments  : — 

Radiation  from  1st  or  thinnest  piece 3.4 

"  '•    2nd  or  middle  piece 4.3 

"  ((    3rd  or  thickest  piece 5.3 

This  proves  that  more  heat  is  radiated  by  a  thick  than  by  a 
thin  piece  of  rock  salt. 

The  following  experiments  were  devised  by  Professor  Forbes, 
to  confirm  the  above  results. 

(a.)  The  second  piece  of  rock  salt  was  placed  obliquely  behind 
the  diaphragm,  making  an  angle  of  20°  with  the  prolongation 
of  the  axis  of  the  cone.  A  piece  of  fir  wood  of  the  same  dimen- 
sions was  placed  in  the  same  way.  The  two  substances  being 
compared  in  this  position,  and  also  in  the  usual  position  behind 

30 


RADIATION   AND   ABSORPTION. 

diaphragm  (viz.,  perpendicular  to  the  direction  of  the  cone's 

axis),  the  following  was  the  result  : 

Oblique.  Usual  position. 

Rock  salt  .36  inch  thick, 4.0  4.0 

Wood,  same  size  as  rock  salt, 9.1  14.1 

In  order  that  this  experiment  may  be  understood,  it  may  be 
well  to  mention,  that,  when  the  plate  was  placed  obliquely  be- 
hind the  diaphragm  it  did  not  quite  fill  up  the  field  of  view. 
Hence  the  wood  gave  out  less  heat  to  the  cone  in  this  than  in 
its  ordinary  position. 

It  appears,  therefore,  that  the  radiation  from  rock  salt,  in  a 
direction  making  a  small  angle  with  the  surface,  bears  a 
greater  proportion  to  the  corresponding  radiation  from  wood 
than  when  both  radiations  are  taken  perpendicular  to  the  sur- 
face. The  reason  undoubtedly  is,  that  in  the  former  case  the 
rays  come  from  a  greater  thickness  of  the  substance,  so  that 
their  intensity  is  increased. 

P.  The  middle-sized  piece  of  rock  salt  was  bound  tightly 
to  the  thickest  piece,  with  a  slip  of  tin  foil  between,  so  that 
the  whole  might  cool  as  one  piece,  and  thus  obviate  any  ob- 
jection that  might  be  brought  against  the  results,  founded  on 
the  unequal  cooling  of  the  plates,  owing  to  their  thicknesses 
being  different. 

The  surface   of  the  middle-sized  piece  facing  the  pile, 

gave 6.3 

That  of  the  thickest  piece,  gave 8.1 

The  plates,  therefore,  still  retain  their  inequality  of  radia- 
tion; but  the  amount  from  each  was  increased,  owing,  no  doubt, 
to  the  reflection  and  radiation  from  the  tin  foil.  The  radiation 
from  the  tin  foil  may  be  estimated  at  1.0,  deducting  which, 
we  have  5.3  and  7.1;  the  increase  now  being  due  to  reflection 
from  the  tin  foil. 

7,  It  thus  appears,  that  while  the  difference  between  the 
radiating  power  of  thick  and  thin  glass  is  so  small  as  not  to  be 
capable  of  being  directly  observed,  there  is  a  perceptible  differ- 
ence between  the  radiation  from  thick  and  thin  mica,  and  a 

31 


MEMOIRS  ON 

still  more  marked  difference  between  the  radiation  from  plates 
of  rock  salt  of  unequal  thickness. 

But  (at  least  with  the  thicknesses  used)  the  greatest  radia- 
tions from  mica  and  rock  salt  were  still  below  that  from  lamp- 
black, and  the  radiation  from  rock  salt  greatly  so. 

The  following  table  exhibits  the  results  of  the  second  group 
of  experiments: 

TABLE  II. 


SUBSTANCE. 

RADIATION  FROM 
THICK  PLATE. 

RADIATION  FROM 
THIN  PLATE. 

Glass      

100 

100 

100 

89 

Rock  salt,  

100 

Middle  »  81 
thin  )  C4 

Third  Group  of  Experiments  described. 

8.  I  now  proceed  to  consider  the  third  group  of  experi- 
ments, or  those  made  with  the  view  of  comparing  the  radiations 
from  various  polished  surfaces  with  that  from  lampblack,  as 
regards  the  quality  of  the  heat;  its  quality  being  tested  by  its 
capability  of  transmission  through  a  screen  of  the  same  mate- 
rial as  the  radiating  plate. 

A.  Glass. — In  an    experiment  already   described,  where   a 
plate  of  crown  glass  .05  inch  thick  was  used  as  a  screen,  and 
a  similar  plate  of  crown  glass  as  a  source  of  heat — 

We  had , 0.95 

A  similar  plate  .1  inch  thick  as  the  source  of  heat, 
gave 1.45 

Blackened  paper  attached  to  a  similar  surface  of  plate 
glass,  .3  inch  thick,  the  blackened  side  being  next 
the  pile, , 1.95 

Therefore  heat  from  a  thin  plate  of  glass  is  less  transmissible 
through  glass  than  heat  from  blackened  paper. 

B.  and  C. — No    experiment  of  this    nature  was  made  with 
alum  or  selenite. 

D.     Mica.  — The  apparatus  already  described  gave — 

32 


K  A  D  I  A  T  1 0  N  AND  ABSORPTION. 

Without    With  mica  screen 
screen.        .0025  inch  thick. 

For  window  (the  window,  it  will 
be  borne  in  mind,  is  the  radia- 
ting surface),  .0009  inch  thick.  .11.2  2.5 

Window  .02  inch  thick 12.7  3.2 

Blackened  paper  attached  to 
glass  lying  on  the  bottom  of 
the  boiling-water  appara- 
tus, gave 21.0  6.3 

We  have  therefore  the  proportion  of  heat  passed  by  mica 
screen 

For  heat  from  thin  mica  window, 223 

"      "    thick    "  "         260 

"      "     blackened  paper,      300 

E.  Rock  salt. — The  thickest  piece  of  rock  salt  (thickness 
.77  inch)  being  used  as  a  screen,  and  the  diaphragm  withdrawn, 
in  order  to  give  greater  results;  the  middle  sized  piece  of  rock 
salt  gave — 

With  screen.     Without  screen 
6.1  19,6 

The  same  screen  stopped  3  rays  out  of  12  for  ordinary  lamp- 
black heat. 

This  experiment  is  sufficient  to  show  that  rock  salt  is  much 
less  diathermanous  for  heat  from  rock  salt  than  for  ordinary 
heat.  The  common  opinion,  that  rock  salt  is  equally  diather- 
manous for  all  descriptions  of  heat,  is  therefore  untenable. 

9.  From  the  third  group  of  experiments  it  appears,  therefore, 
that  heat  emitted  by  glass,  mica,   or  rock  salt,  is  less   trans- 
missible through  a  screen  of  the  same  material  as  the  heated 
plate,    than  heat  from  lampblack ;  this  difference  being  very 
marked  in  the  case  of  rock  salt. 

Fourth  Group  of  Experiments  described. 

10.  1  now  proceed  to  the  fourth  group  of   experiments,  or 
those  made  with  the  view  of  comparing  the  radiations  of  plates 
of  the  same  substance,  but  of  different  thicknesses,  with  regard 
to  the  quality  of  the  heat  radiated. 

33 


MEMOIKS     ON 

A.  Glass. — It  has  been  already  shown   (Art.  8),   that   heat 
from  crown  glass  .05  inch  thick  is  less  transmissible  through 
glass,  than  that  from  crown  glass  .10  inch  thick. 

B.  and  0. — No  experiments  of  the   kind  were  made  on  alum 
or  selenite. 

D.  Mica. — It  has  been  already  shown  (Art.  8),  that  heat  from 
thin  mica  is  less  transmissible  through  a  mica  screen  than  heat 
from  thick  mica. 

E.  Rock  salt. — With  a  screen  of  rock  salt  .18  inch  thick,  the 
following  result  was  obtained  : 

Thickest  piece  of  rock  salt,  heated  to  210° 

(thickness  .77  inch),  gave 2.5 

Middle-sized  piece  of  rock  salt,  heated  to  210° 

(thickness  .36  inch),  gave 1.7 

Thinnest  piece  of  rock  salt,  heated  to  210° 

(thickness  .18  inch),  gave 1.1 

Without  any  screen,  the  same  pieces  gave — 

Thickest, 4.9 

Middle-sized, 4.1 

Thinnest, 3.3 

Proportion  of  heat  from  thickest  piece  passed 51 

Proportion  of  heat  from  middle-sized  piece  passed    .41 

Proportion  of  heat  from  thinnest  piece  passed 33 

A  similar  experiment,  with  a  screen  .29  inch  thick  gave — 

With  screen.     Without  screen.     Proportion  passed. 

Thickest    piece. .  .2.6  5.4  .48 

Middle-sized,  ....1.8  4.5  .40 

Thinnest 1.2  3.5  .33 

It  follows  from  this,  that  a  screen  of  rock  salt  passes  heat 
from  thick,  more  easily  than  heat  from  thin  rock  salt, 

11.  From  this  fourth  group  of  experiments,  we  learn  that  heat 
from  thick  plates  of  glass,  mica,  or  rock  salt,  is  more  easily 
transmitted  by  screens  of  the  same  nature  as  the  heated  plate 
than  heat  from  thin  plates  of  these  materials. 

The  following  table  exhibits  the  results  of  the  third  and 
fourth  group  of  experiments  : 


RADIATION   A  K  D  •  A  B  S  0  E  P  T  I  0  K . 


TABLE  III. 


No.  of  Rays  out  of  every 
100  that  pass  through 
a  screen   of  the   same 

No.  of  Rays  of 
Lampblack 
Heat  out  of 

SOUBCE  OF  HEAT. 

material  as  the  source 
of  Heat  in  1st  column, 

every   100 

the    screen    being     of 
only  one  thickness  for 

that    pass 
through  the 

each  material. 

same  screen 

Glass  (crown  ^th  inch  thick), 

0.66) 

1.33 

Glass  (crown  ^th  inch  thick), 

1.0   } 

Mica  (thickness  .0009  inch), 

22. 

Mica  (thickness  .02  inch), 

2GJ 

30 

Rock  salt  (thickness  .18  inch), 

33) 

(Art.  12) 

Rock  salt  (thickness  .36  inch), 

41  [ 

82 

Rock  salt  (thickness  .77  inch), 

50* 

Lamp 


Results  deducible  from  the  foregoing  Experiments. 

12.  These  experiments,  as  well  as  others  yet  to  be  described, 
may  be  explained  by  Prevost's  theory  of  exchanges,  somewhat 
modified. 

In  the  first  place,  it  would  seem  to  be  a  consequence  of  this 
theory,  that  radiation  must  take  place  from  the  interior  as  well 
as  from  the  surfaces  of  bodies.  For,  suppose  that  we  have  two 

indefinitely  extended  surfaces  of 
lampblack,  as  in  the  figure,  and 
between  them  a  plate  of  rock 
salt  of  a  certain  thickness,  also 
indefinitely  extended;  and  let 
the  whole  be  kept  at  the  same 
temperature.  Then,  since  the 
temperature  of  the.  rock  salt 
remains  the  same,  it  must  radiate 
as  much  as  it  absorbs.  But  a  thicker  plate  of  rock  salt,  placed 
under  the  same  circumstances,  would  absorb  more  of  the  heat 
radiated  from  the  lampblack  because  each  ray  would  have  to 
pass  through  a  greater  depth  of  the  substance  of  salt;  hence  a 
thick  plate  of  rock  salt  must  radiate  more  than  a  thin  plate. 
We  see  likewise,  the  reason  for  the  small  radiative  capacity  of 

35 


MEM'OIRS     ON 

rock  salt  to  be  its  small  absorptive  capacity.  In  order  to  prove 
this  deduction  from  Prevost's  theory  experimentally  true,  the 
following  experiment  was  devised: 

A  boiling-water  canister,  coated  with  lampblack,  was  put 
behind  the  diaphragm,  filling  up  the  field  of  view,  and  the 
three  pieces  of  rock  salt  heretofore  used  as  sources  of  heat, 
were  now  separately  used  as  screens,  being  put  before  the  dia- 
phragm, so  that  the  heat  from  the  canister  had  to  pass 
through  their  substance  before  reaching  the  cone.  The  follow- 
ing was  the  result: 

Without  any    Screen  of  Screen  of  Screen  of 

screen.        Rock  salt  Rock  salt  Rock  salt 

.18  inch  .36  inch  .77  inch 

thick.  thick.          thick. 

Eadiation  from  canister,     21.3  17.6  16.8  15.8 

The  difference  between  heat  absorbed  by  plate, 
thickness  =  .18  inch,  and  that  absorbed  by 
plate,  thickness  =  .36  inch, 

is 1.2) 

Another  similar  experiment  gives 0.9  J     Mean  *•! 

The  difference  between  heat  absorbed  by  plate, 
thickness  =  .36  inch  and  that  absorbed  by 
plate,  thickness  =  .77  inch, 

is 1.0  ) 

Another  similar  experiment  gives 1.3  f     Mean  1.1 

These  should  nearly  correspond  to  the  differences  between  the 
radiation  from  the  same  place,  under  their  ordinary  circum- 
stances of  position  (if  the  theory  be  true  which  asserts  that  the 
absorption  of  such  a  plate  equals  its  radiation);  accordingly  we 
find  that 

The    difference     between    heat    radiated     by 

plate,  thickness =  .18  inch    )    -.- 

And  that  radiated  by  plate  thickness  =  .36  inch,  ) 
While    the   difference    between    radiation   of 

plate  thickness =  .36  inch    } 

And  that  of  plate  thickness =  .77  inch,  f    Is  1<0 

(Art.  6,  mean  of  four  sets  of  experiments.) 
We  see,  therefore,  that  there  is  an  agreement  between  the 
two  sets  of  differences,  as  near  as  can  be  reasonably  expected. 

36 


RADIATION   AND   ABSORPTION. 


13.  If  we  now  suppose  a  plate  of  glass,  arid  not   a  plate  of 
rock   salt,    placed   between    surfaces   of  lampblack,  the  plate, 
whether   thin    or  thick,  will  allow   scarcely  any  heat  to  pass 
through  it;   and,  consequently,  plates  of  different  thicknesses 
will   all   absorb  very  nearly  the  same  amount,  that  is,  nearly 
all  that  enters  them.     In  this   case,   therefore,  the  radiation 
(which  is  equal  to  the  absorption)  will  be  very  slightly  increased 
by  an  increase  of  thickness  of  the  plate.     Also  the  amount  of 
heat  radiated,  being  equal  to  the  heat  absorbed,  will  be  very 
nearly  as  great  as  that  from  lampblack. 

14.  There  are,  therefore,  two  peculiarities  of  the  radiation 
from  plates  of  diathermanous  substances,  and  which  are  most 
marked  for  those  substances  which  are  most  diathermanons. 

1st,  That  the  amount  of  radiation  from  such  plates  is  less 
than  that  from  lampblack. 

2d,  That  the  amount  of  radiation  from  such  plates  increases 
with  the  thickness  of  the  plate. 

The  correlation  between  these  different  properties  of  bodies 
is  seen  from  the  following  table: 

TABLE  IV. 


Bodies  ranked  according 
to  their  Radiating  Ca 
pacity  (least  radiating 

Bodies    ranked    ac- 
cording   to    their 
Diathermancy 
(most  diatherman- 

Bodies  ranked  according 
to   the    proportion   by 
which  their  Radiation 
is  increased  by  increas- 

first). 

ous  first). 

ing  the  thickness. 

A  stratum  of  heated  gas 

(from  Melloni's  Exper- 

iments), 

A  stratum  of  gas. 

Rock  salt. 

Rock  salt. 

Rock  salt. 

Mica. 

Mica. 

Mica. 

Glass.       j 

Glass.       ^ 

Glass. 

Selenite.  > 

Selenite.  ? 

.... 

Alum.       ) 

Alum. 

15.  The  reason  why  radiation  has  hitherto  been  supposed  to 
be -confined  to  the  surface,  or  to  an  exceedingly  small  distance 
below  the  surface  of  a  body  now  becomes  obvious.  The  effect  of 
coating  a  surface  of  polished  metal  with  gum,  for  instance,  is 

37 


MEMOIRS     ON 

to  increase  the  radiation;  but,  after  a  very  small  thickness  of 
film,  an  additional  coating  is  powerless  to  increase  the  radiation; 
the  reason  being,  not  that  radiation  is  incapable,  in  all  cases,  of 
taking  place  except  at  the  surface;  but  because  such  films  be- 
ing exceedingly  impervious  to  heat  of  low  temperatures,  the 
radiation  from  them  is  very  little  increased  by  increasing  their 
thickness. 

Since,  therefore,  it  appears  that  radiation  takes  place  from 
the  interior  as  well  as  from  the  surface  of  bodies,  the  question 
arises,  are  we  to  suppose  each  particle  of  each  substance  to 
have,  at  a  given  temperature  an  independent  radiation  of  its 
own,  equal,  of  course,  in  all  directions  ?  A  priori,  this  is  the 
most  probable  supposition,  and  it  seems  likewise  to  be  conform- 
able to  experiment. 

16.  In  an  experiment  already  described, 

A  plate  of  crown  glass  .05  inch  in  thickness  being  used  as 
a  screen,  the  quantity  of  heat  radiated  from  crown 
glass  .05  inch  thick  that  passed,  was 0.95 

While  of  that  radiated  from  crown  glass,  .10  inch  thick 
there  passed 1.45 

Another  experiment  gave — 

Quantity  of  heat  from  crown  glass  .05  there  passed  .  .1.1 

Quantity  radiated  from  two  plates  of  crown  glass,  each 
.05  inch  thick  the  one  placed  loosely  behind  the 
other, 1.55 

From  this  we  may  infer,  that  the  radiation  from  two  plates 
of  glass  placed  loosely  behind  each  other  is  the  same  as  the  ra- 
diation from  a  plate  of  double  the  thickness,  and,  consequently, 
that  the  radiation  from  a  particle  of  a  substance  does  not  di- 
minish owing  to  its  being  placed  in  the  interior.* 

17.  Let  us  now  refer  to  the  radiation  from  rock  salt: 

The  radiation  from  a  piece  .18  inch  thick,  was 3.4 

That  from  a  piece  .36  inch  thick,  was 4.3 

That  from  a  piece  .77  inch  thick,  was 5.3 

*  The  idea  of  this  experiment  was  derived  from  a  remark  of  Professor 
Forbes,  who  suggested  that  several  plates  of  rock  salt,  the  one  behind 
the  other,  might  be  advantageously  substituted  for  a  thick  plate  of  the 
same  material  as  giving  the  very  same  result. 

38 


RADIATION  AND  ABSORPTION. 

Now  if  we  suppose  the  radiation  of  a  particle  in  the  interior 
to  be  as  intense  as  that  of  a  particle  at  the  surface,  why,  it  may 
be  asked  (since  rock  salt  is  extremely  diathermanous),  does  not 
a  piece  of  double  thickness  give  nearly  a  double  radiation  and 
so  on,  the  radiation  increasing  very  nearly  as  the  thickness  ? 

If  we  still  hold  the  doctrine  of  an  equal  and  independent  ra- 
diation from  every  particle,  we  are  shut  up  to  the  conclusion 
that  rock  salt  must  be  comparatively  opaque  to  heat  radiated 
by  itself,  a  result  which  is  abundantly  confirmed  by  experiment. 

Thus  while  the  radiation  from  rock  salt  .18  inch  thick,  with- 
out any  screen,  is  3.4,  with  a  screen  of  rock  salt  .18  inch  thick 
it  becomes  1.1. 

If,  therefore,  we  have  a  piece  of  rock  salt  of  double  the 
thickness,  or  .36  inch  thick,  we  should  expect  that  the  radia- 
tion from  it  would  be  =  3.4  +  1.1  =  4. 5.  It  is,  in  fact,  4.3.  The 
difference  (0.2)  being  within  the  limit  of  error  of  observation. 

In  rock  salt,  therefore,  we  may  suppose  each  particle  to  have 
an  independent  radiation  of  its  own,  unaffected  by  its  distance 
from  the  surface. 

18.  We  see,  therefore,  that  the  opacity  of  rock  salt  with  re- 
gard to  heat  radiated  by  itself,  is  a  consequent  of  the  admis- 
sion, that  the  radiation  from  rock  salt  does  not  increase  so 
rapidly  as  the  thickness  increases  ;  ar.d  this  again  results  from 
the  fact,  that  the  absorption  of  heat  by  a  plate  of  rock  salt 
does  not  increase  so  rapidly  as  the  thickness  increases.  This, 
again,  is  due  to  the  fact,  that  the  first  part  of  the  plate  of  rock 
salt  sifts  the  heat  so  that  it  is  more  easily  transmitted  by  the 
second  part;  and  this  confirms  the  result  arrived  at  by  Professor 
Forbes,  who,  finding  that  rock  salt  stopped  heat  of  lower  tem- 
perature rather  more  readily  than  heat  of  high  temperature, 
concluded  that  there  are  a  few  rays  for  which  rock  salt  is 
opaque.* 


*  To  take  a  numerical  example,  let  us  suppose  the  heat  from  a  single 
plate  of  rock  salt  to  be  =  1,  then  the  heat  from  a  plate  four  times  the 
thickness,  or  (which  is  the  same  thing)  the  heat  from  four  single  plates, 
one  behind  another,  should  be  nearly  four  times  as  much  or  =  4  (if  we 
suppose  the  heat  from  each  of  these  four  plates  to  be  readily  passed  by 
the  plates  between  it  and  the  pile),  but  the  heat  from  the  four-fold 
plates,  instead  of  being  four  times  as  much,  is  not  double  of  the  heat 

39 


MEMOIRS     ON 

We  conclude,  therefore,  that  every  body  which  sifts  heat  in 
its  passage  through  its  substance  is  more  opaque  with  regard 
to  heat  radiated  by  a  thin  slice  of  its  own  substance,  than  it  is 
with  regard  to  ordinary  heat. 

19.  This  conclusion  may  be  also  stated  thus:  We  have  before 
proved  (Art.  12)  that  the  radiation  of  a  thin  slice  of  any  sub- 
stance equals  its  absorption;  we  now  add  that  the  heat  radiated 
is  the  same  as  that  absorbed,  with  regard  to   quality  as  well 
as  quantity. 

For  this  expresses  the  fact,  that  substances  which  sift  heat 
are  likewise  opaque  with  respect  to  heat  radiated  by  themselves. 
For,  since  the  heat  which  they  absorb  is  manifestly  that  kind 
of  heat  for  which  they  are  opaque,  if  the  description  of  heat 
radiated  is  the  same  as  that  absorbed,  then  they  also  will  be 
opaque  with  respect  to  heat  radiated  by  themselves.  Consid- 
ering, therefore,  the  heat  of  any  temperature  to  consist  of 
heterogeneous  rays,  we  may  state  the  law  thus  :  "  The  absorp- 
tion of  a  plate  equals  its  radiation,  and  that  for  every  descrip- 
tion of  heat.  " 

20.  A    more   rigid  demonstration  may  be  given  thus:  Let 
AB,  and  EC  be  two  contiguous,  equal,  and  similar  plates  in  the 
interior  of  a  substance  of  indefinite  extent,  kept  nt  a  uniform 
temperature.    The  accumulated  radiation  from  D 

the  interior  impinges  on  the  upper  surface  of 

the  upper  plate;  let  us  take  that  portion  of  it  - A! , 

which  falls  on  the  particle  A,  in  the  direction  B| 

DA.  This  ray,  in  passing  from  A  to  B,  will  have  | 

been  partly  absorbed  by  the  substance  between 
A  and  B,  but  the  radiation  of  the  upper  plate  being  equal  to  its 
absorption  (since  its  temperature  remains  the  same),  the  ray  will 
have  been  just  as  much  recruited  by  the  united  radiation  of  the 

from  the  single  plate  ;  hence,  the  heat  from  any  of  the  interior  plates  of 
the  compound  plate  is  passed  with  great  loss,  by  the  plates  between  it 
and  the  pile.  Now,  since  the  absorption  of  a  plate  equals  its  radiation, 
the  reason  why  the  four-fold  plate  scarcely  radiates  twice  so  much  as 
the  single  one  is,  that  it  scarcely  absorbs  twice  as  much;  and  this  again 
is  due  to  the  fact,  that  the  heat  after  it  has  passed  the  first  plate  of  the 
four-fold  plate  has  become  sifted,  and  passes  with  little  diminution  of 
intensity  through  the  other  three  plates. 

40 


RADIATION   AND   ABSORPTION. 

particles  between  A  and  B,  as  it  was  diminished  in  intensity  by 
their  absorption.  It  will  therefore  reach  B  with  the  same 
intensity  it  had  at  A.  But  the  quality  of  the  ray  at  B  will  also 
be  the  same  as  its  quality  at  A.  For,  if  it  were  different,  then 
either  a  greater  or  less  proportion  would  be  absorbed  in  its  pas- 
sage from  B  to  C,  than  was  absorbed  of  the  equally  intense  ray 
at  A,  in  its  passage  between  A  and  B.  The  amount  of  heat  ab- 
sorbed by  the  particles  between  B  and  0  would  therefore  be 
different  from  that  absorbed  by  the  particles  between  A  and  B. 
But  this  can  not  be;  for,  on  the  hypothesis  of  an  equal  and  in- 
dependent radiation  of  each  particle,  the  radiation  of  the  parti- 
cles between  B  and  C  is  equal  to  that  of  the  particles  between  A 
and  B,  and  their  absorption  equals  their  radiation.  Hence  the 
radiation  impinging  on  B,  in  the  direction  of  DB,  must  be 
equal  in  quality  as  well  as  in  quantity  to  that  impinging  upon 
A;  and,  consequently,  the  radiation  of  the  particles  between 
A  and  B  must  be  equal  to  their  absorption,  as  regards  quality 
as  well  as  quantity;  that  is,  this  equality  between  the  radiation 
and  absorption  must  hold  for  every  individual  description  of 
heat. 

21.     The  following  experiment  illustrates  this  law: 

The  quantity  of  heat  radiated  from  crown  glass  screen, 
.05  inch  thick,  which  passes  through  a  crown  glass 
screen  .05  inch  thick,  . . . . , =  0.95 

While  that  from  plate  glass  .3  inch  thick,  covered  with 
blackened  paper  (the  blackened  paper  being  next  the 
pile),  which  passes  through  the  same  screen.  ..  =  1.95 

But  if  the  surface  of  crown  glass  .05  inch  thick,  farthest 
from  the  pile,  be  coated  with  paper,  the  polished  sur- 
face being  next  the  pile,  then  the  amount  which  passes 
the  screen, =  1.85 

And  if  three  plates,  the  one  behind  the  other,  of  crown 
glass,  each  .05  inch  thick,  be  used  as  the  source  of 
heat,  the  surface  farthest  from  the  pile  of  the  farthest 
off  plate  only  being  covered  with  paper,  the  amount 
of  radiation  which  passes  the  screen, =  1.95 

Such  a  plate  of  glass  or  series  of  plates,  therefore,  by  having 
the  farthest   off   surface  coated    with   paper,    gives   out    heat 

41 


MEMOIRS  ON 

similar  to  that  from  paper  or  lampblack;  the  reason  being, 
that  the  heat  from  the  paper  on  the  farthest  off  surface  is  as 
much  recruited  as  it  is  absorbed  by  its  passage  through  the 
glass,  both  as  regards  quantity  and  quality;  so  that  the  radia- 
tion which  falls  upon  the  cone  is  virtually  that  from  paper  or 
lampblack. 

23.  There  is  little  difficulty  in  explaining  why  heat  from  a 
thick  plate  of  any  substance  should  pass  more  readily  through 
a  screen  of  the  same  substance  than  that  from  a  thin  plate. 
The  reason  is,  that  the  heat  from  the  interior  of  the  thick 
substance,  having  been  sifted  in  its  passage,  is,  therefore,  now 
more  easily  able  to  pass  through  a  screen  of  the  same  substance. 

23.  We  see  also  why,  generally  speaking,  bodies  at  the  same 
temperature   radiate   the   same  quality  of  heat;  let  us,  for  in- 
stance, take  a  tolerably  thick  plate  of  glass,  and  a  surface  of 
lampblack,    and  compare  them  together.     Since  the  plate  of 
glass  absorbs  nearly  all  the  rays  that  fall  upon  it,  it  will  radiate 
nearly  as  much  as   lampblack;    and  since  the  quality  of   the 
radiated  is  the  same  as  the  quality  of  the  absorbed  heat,  its 
radiated  heat  will  very  nearly  have  the  same   quality  as  that 
which  is  radiated  by  lampblack. 

Tlie  influence  of  the  Reflective  and  Refractive  Powers  of  Bod- 
ies on  their  Radiation  considered. 

24.  Hitherto  in  these  investigations  no  account  has  been  taken 
of  reflection  at  the  surfaces  of  the  plates, because — 1st,  those  rays 
only  were  considered  which  passed  perpendicularly,  or  nearly  so, 
through  such  plates  ;  and,  2d,  because  the  indexes  of  the  re- 
fraction for  the  substances  experimented  on  were  not  very  high. 

But  for  rays  passing  obliquely  through  such  media,  or  for 
rays  passing  in  any  direction  into  substances  such  as  metals,  we 
must  take  account  of  reflection  from  the  surface  which  will  in- 
fluenoe  materially  our  results. 

Thus,  no  substance  is  so  opaque  for  heat  as  metals,  but  yet 
only  a  small  portion  of  the  heat  falling  on  them  is  absorbed, 
the  rest  being  reflected  back  ;  consequently  for  such  bodies  the 
radiation  (which  must  be  equal  to  the  absorption)  is  very  small. 

It  is  also  desirable,  for  another  reason,  to  investigate  the 
laws  according  to  which  the  reflective  nature  of  the  surface  of 

42 


RADIATION   AND   ABSORPTION. 


a  body  influences  its  radiation.  For  the  question  arises,  is  the 
law  of  an  equal  and  independent  radiation  of  each  particle  of  a 
body  theoretically  consistent  with  equilibrium  of  temperature  ? 
That  is,  suppose  we  have  an  irregularly-shaped  inclosure  walled 
round  with  a  variety  of  substances,  and  each  particle  of  each 
substance  radiating  into  the  inclosure,  from  the  sides  of  which 
it  is  reflected  many  times  backwards  and  forwards  before  it  is 
finally  absorbed  ;  this  being  the  case,  will  the  law  of  equal  and 
independent  radiation,  and  those  of  reflection  and  refraction, 
so  fit  with  one  another,  that  every  particle  of  the  walls  of  the 
inclosure  shall  absorb  precisely  as  much  heat  as  it  radiates  ? 
It  will  be  endeavored  to  show  that  these  laws  are  so  adapted  to 
each  other ;  and  I  shall  select  for  the  proof  a  definite  form  and 
description  of  inclosure,  the  conclusions  arrived  at  rendering  it 
highly  probable  (if  not  rigidly  demonstrating)  that  the  same 
adaptation  will  hold  good  for  every  inclosure,  however  irregular 
or  varied. 

For  these  reasons,  I  shall  now  endeavor  to  investigate  what 
connection  the  radiation  of  a  substance  has  with  the  reflective 
power  of  its  surface  ;  and  in  doing  so  (in  order  to  abstract 
entirely  from  the  effects  produced  by  the  variable  thickness  of 
the  radiating  plate),  I  shall  suppose  it  to  be  of  indefinite  thick- 
ness ;  so  that  all  the  heat  which  enters  it  is  absorbed.  Our 
consideration  is,  therefore,  limited  to  the  effects  of  one  surface. 

25.  Let  AB  be  a  portion 

Lamp  B!ack  of  the  line  of  section  of  an 

indefinitely  extended  sur- 
face with  the  plane  of  the 
paper  supposed  perpendicu- 
lar to  the  surface,  and  let 
this  surface  belong  to  a 
body  (M)  of  indefinite 
thickness  downwards ;  also 
let  there  be  an  indefinitely 
extended  surface  of  lamp- 
black parallel  to  this  lower  surface,  as  in  the  figure.  Lastly, 
let  the  whole  be  kept  at  uniform  temperature.  In  order  that 
the  body  (M)  may  be  maintained  at  this  temperature,  it  is 
necessary  that  the  heat  which  has  left  the  surface  AB,  having 

43 


MEMOIRS  ON 


come  from  the  interior  of  (M),  in  the  direction  contaiued*in 
any  very  small  angle  CAD,  shall  be  replaced  by  an  equal  quantity 
of  heat  entering  the  surface  AB,  to  diverge  into  the  interior 
through  the  same  small  angle  CAD.  For,  by  this  arrangement 
it  is  clear  the  particles  in  CAD  get  back  as  much  heat  as  they 
give  out. 

Part  of  the  heat,  no  doubt,  which  fell  on  A  in  any  direction 
DA,  would  be  reflected  back  in  the  direction  AD',  making  the 
same  angle  with  the  surface  as  AD  ;  but  this  loss  would  be 
made  up  for  by  part  of  the  heat  falling  upon  A,  in  the  direction 
D'A,  being  also  reflected  back  in  the  direction  AD. 

The  internal  reflection  at  A  being  compensated  for,  if  the 
heat  that  really  leaves  the  medium  be  also  compensated  for, 
then  as  much  heat  will  be  passing  at  A  in  the  direction  AD  as 
will  be  passing  in  the  direction  DA.  It  will  be  the  same, 
therefore,  as  if  the  body,  instead  of  having  a  surface  at  A, 
were  indefinitely  extended  upwards  from  A,  as  well  as  down- 
ward ;  in  which  case,  as  has  been  already  shown  (Art.  20),  there 
will  be  equilibrium  of  temperature,  provided  that  the  radiation 
of  a  particle  is  equal  to  its  absorption,  and  that  for  every  des- 
cription of  heat. 

Before  proceeding  further  with  this  investigation,  it  will  be 
necessary  to  establish  some  preliminary  propositions. 

26.  1st  Preliminary  Proposition. 

The  heat  which  falls  on  the  line  AB  in  the  directions  con- 
tained in  the  very  small  angle  CAD,  is 
the  same  which  falls  on  AE,  perpendic- 
ular, EB,  through  the  same  very  small 
angle.  For  every  ray  which  fell  on  AB 
passed  through  AE,  with  the  exception 
of  a  small  quantity  which  passed  through 
B  EF  ;  but  the  angle  EBF  being  very 

small,  EF  is  very  small  compared  with  AE,  and  consequently 
the  heat  falling  on  EF  may  be  neglected  in  comparison  with 
that  falling  on  AE. 

It  is  clear,  also,  that  the  heat  falling  on  AB  is  proportional  to 
AB,  and  to  the  size  of  the  very  small  angle  CAD. 

The  above  will  still  hold  if,  instead  of  the  substance  of  which 
AB  is  the  surface  being  supposed  below  AB,  and  the  rays  fall- 

44 


RADIATION   AND   ABSORPTION. 

ing  on  it  through  a  vacuum,  we  suppose  a  substance  to  be 
indefinitely  extended  upward  and  the  rays  to  originate  in  the 
substance  itself,  and  fall  on  its  surface  AB. 

For,  although  any  ray  GE,  which  falls  on  E,  will  be  partly 
absorbed  between  E  and  B,  it  will  be  as  much  recruited  by  the 
united  radiation  of  the  particles  between  E  and  B  as  it  was 
absorbed  ;  so  far,  indeed,  as  regards  quality  and  intensity  (from 
what  has  been  already  proved,  Art.  20),  we  may  consider  such 
a  ray  to  be  traversing  a  vacuum,  it  being  recruited  just  in  pro- 
portion as  it  is  absorbed. 

It  is  evident,  also,  that  in  this  case  the  quantity  of  heat  fall- 
ing on  AB  will  be  proportional  to  the  size  of  the  very  small 
angle  CAD. 

27.     2d  Proposition. 

First  case. — If  AB  represent  a  surface  (the  substance  being 

below  AB),  and  OF  a  surface  of   lamp-  c    p G    F 

black  indefinitely  extended  (as  in  Art. 
25),  from  which  rays  fall  on  AB  through 
a  small  angle  CAD  ;  then,  if  AE  be 
drawn  perpendicular  to  GB,  the  heat 
that  falls  on  AB  will  =  a  const.  X  AE, 
whatever  be  the  value  of  the  angle  CAB. 

For,  since  the  angle  CAD  is  exceedingly  small,  CD  may  be 
considered  very  small  in  comparison  with  CF  or  CG ;  therefore 
the  heat  which  impinges  on  AB  through  the  angle  CAD  may 
be  taken  to  be  that  which  radiates  from  CG  in  direction  between 
CA  and  DA;  but  since  the  radiative  power  of  lampblack  in 
any  direction  varies  as  the  sine  of  the  angle  which  that  direction 
makes  with  the  surface,  this  will  =  const.  X  AE.  Hence,  if 
R  X  CAD  be  the  quantity  of  heat  which  falls  on  AB,  when  AB 
is  perpendicular  to  GB,  that  which  falls  on  it  when  GB  makes 
any  angle  GBA  with  AB.  will  be  R  X  CAD  sin  GBA. 

If  i  denote  the  angle  which  GB  makes  with  the  perpendicu- 
lar to  AB,  then  the  heat  impinging  on  AB  will  be  R  cos  i 
X  CAD. 

2d  case. — If  the  substance  be  above  AB,  and  the  rays  falling 
on  AB  originate  in  the  substance,  the  same  formula  will  hold, 
for  it  has  been  shown,  in  Prop.  1st,  that  in  this  case,  the  heat 
falling  on  AB  through  the  small  angle  CAD  =  that  which  falls 

45 


MEMOIRS    ON 

on  AE  through  the  same  small  angle;  but,  since  the  radiation 
from  the  interior  of  the  substance  is  the  same  in  all  directions 
(each  particle  radiating  independently  and  equally  in  all  direc- 
tions), the  amount  falling  on  AE  will  not  be  aifected  by  the 
angle  which  AE  makes  with  the  surface;  hence  the  heat  falling 
on  AB  =  const.  X  AE  =  const.  X  sin  GBA. 

If  R'  X  CAD  =  quantity  which  falls  on  AB  when  AB  is  per- 
pendicular to  GB,  that  which  falls  on  it  when  GB  makes  any 
angle  GBA  with  AB,  will  be  R'  X  CAD  sin  GBA  ;  also  the 
expression  corresponding  to  R  cos  i'  x  CAD  will  be  R'  cos  i' 
XCAD. 

28.  3d  Proposition.  Let  a  ray  strike  the  surface  of  a  me- 
dium, at  an  angle  of  incidence  =  i;  and  another  ray  at  an  angle 
of  incidence  i  +  6  i,  it  is  required  to  find  the  difference  between 
the  two  angles  of  refraction. 

Let  p  be  the  index  of  refraction,  then, 

sin  i==  fj.  sin  i' 

Hence,  6  (sin  i)  =  p  6  (sin  if) 

cos  i  6  i  =  ft  cos  i'  6  i' 

TT  .,      cos  i 

Hence,  6  ^—  -    —  r,s  i 


29.  I  shall  also  make  the  following  supposition  with  regard 
to  the  laws  of  reflection  and  refraction. 

1st.  That  if  Q  represent  the  quantity  of  heat  falling  on  the 
surface  of  a  medium  in  any  direction  CA,  and 
0Q  be  the  quantity  reflected,  then  (1  —  a)  Q  is  the 
quantity  of  heat  refracted  into  the  medium  in 
the  direction  AC7.  This  follows  from  the  law  of 
the  conservation  of  vis  viva. 

2d.  That  if  the  same  heat  Q  originate  in  the 
Ic1  medium,  and  strike  A  in  the  direction  C'A, 
the  quantity  reflected  back  into  the  medium  will  be  #Q,  and 
the  quantity  refracted  out  in  the  direction  AC  will  be  (1  —  a)  Q. 

30.  These  preliminary  propositions  being  established,  and 
suppositions  made,  let  us  suppose  that  heat  from  the  surface  of 
lampblack  strikes  the  surface  AB  of  the  indefinitely  thick  me- 
dium (Fig.  Art.  25)  through  a  small  angle  6i  (i  being  the  angle 
of  incidence),    by  Prop.   2d.    the   Quantity  of  this   heat  will 

46 


RADIATION    AND    ABSORPTION. 

be  R  cos  idi;  while  the  part  of  it  which  enters  the  substance 
we  shall  call  (1 — a)  R  cos  i  6  i.  These  rays  will  diverge  in  the 

f»f)Q      -1 

substance  through  an  angle  6  i'=  • —  ^— r  6  i  (Prop.  3). 

p  COS   I 

But  the  quantity  of  heat  that  falls  on  AB  from  the  interior 
through  this  angle  will  be 

R'  cos  idi'  =  R'  cos  i'  -uc°*s\,  *i  =  ~-  cos  iti, 

and  the  portion  of  this  which  leaves  the  medium  will  be 
(1-a)  R'  cos  ;'  di 

* 

Equating  this  with  (I— a)  R  cos  161,  which  enters  the  me- 

R' 

dium,  we  have  —  =•  R  or  R  '=  /"  R.     With  this   supposition, 

/* 

therefore,  the  law  of  an  equal  and  independent  radiation  of 
each  particle  will  give  us  equilibrium  of  temperature  in  the 
particular  case  under  consideration.  Had  R'  been  a  function 
of  i',  it  would  have  shown  that  the  law  of  an  equal  an  inde- 
pendent radiation  was  inconsistent  with  equilibrium  of  tem- 
perature. 

31.  Only  part,  however,  of  the  heat  from   the  lampblack 
falling  on  AB  entered  into  the  medium,  a  portion  of  it  =  a  R 
cos  i  6  i  being  reflected  back  to  the  lampblack,  hence  the   total 
quantity  of  heat  radiated  and  reflected  which  leaves  the  surface 
AB  through  the  small  angle  di  will  be  =  R  cos  i  6  i,  the  same  as 
if  the  substance  had  been  lampblack,  the  only  difference  being, 
that,   in   the   case   of     lampblack,   all  this   heat  is  radiated, 
whereas  in  other  substances  only  part  is  radiated,  the  remainder 
being  reflected  heat. 

32.  Although  we  have  considered  only  one  particular  case, 
yet  this  is  quite  sufficient  to  make  the  general  principle  plain. 
Let  us  suppose  we  have  an  enclosure  whose  walls  are  of  any 
shape,  or  any  variety  of  substances  (all  at  a  uniform  temper- 
ature), the  normal  or  statical  condition  will  be,  that  the  heat 
radiated  and  reflected  together,  which  leaves  any  portion  of  the 
surface,  shall  be  equal  to  the  radiated  heat  which  would  have 
left  that  same  portion  of  the  surface,  if  it  had  been  composed 

47 


MEMOIRS  ON 

of  lampblack.  And,  indeed,  we  may  see,  from  what  has  been 
already  proved,  that  should  such  a  state  of  things  only  once 
take  place,  it  would  always  remain,  there  being  no  disposition 
to  alter  it. 

Let  us  suppose,  for  instance,  that  the  walls  of  this  enclosure 
were  of  polished  metal,  then  only  a  very  small  quantity  of  heat 
would  be  radiated  ;  but  this  heat  would  be  bandied  backwards 
and  forwards  between  the  surfaces,  until  the  total  amount  of 
radiated  and  reflected  heat  together  became  equal  to  the  radia- 
tion of  lampblack.* 

33.  The  equation  R'  =  //R  must  necessarily  hold  for  every  in- 
dividual description  of  heat.  We  have,  therefore,  two  laws 
necessary  to  the  equilibrium  of  temperature — 1st,  That  the 
absorption  of  a  particle  is  equal  to  its  radiation,  and  that  for 
every  description  of  heat  ;  2d,  That  the  flow  of  heat  from  the 
interior  upon  the  surface  of  a  substance  of  indefinite  thickness, 
is  proportional  caeteris  paribus  to  its  index  of  refraction  and 
that  for  every  description  of  heat.  It  will,  however,  be  borne 
in  mind,  that  the  former  of  these  laws  has  been  verified  by  ex- 

*  This  will  be  clearly  seen  if  we  consider  only  those 

rays  that  are  radiated  perpendicular  to  the  surface 
to  the  case  of  two  parallel  plates  of  polished  metal 
~~  of  the  same  description  radiating  to  one  another. 
For  let  r  be  the  common  radiation  of  the  point  C  in  direction  CD,  and 
of  the  point  D  in  the  direction  DC,  then  since  these  radiations  are 
bandied  backwards  and  forwards  in  the  directions  CD,  DC.  until  they 
are  extinguished,  we  have  the  total  quantity  of  heat  falling  on  D  in  the 
direction  CD  (if  ar  denote  the  proportion  of  r  reflected  after  one  single 
reflection)  expressed  as  follows: 

Total  heat  radi-  J       (     r+aV+aV+etc,    )  =  r(l+a+^+a8) 

ated  and  reflected,  P—4  +ar+a8r+«Br+etc.  f  =  —  (since  a  <  1) 
falling  on  D,      )       (  )      1— a v 

But  1 — a  denotes  the  absorptive  power  of  the  metallic  surface  (all  the 
heat  not  reflected  being  absorbed).  Hence,  since  the  radiative  powers 
of  bodies  are  proportional  to  their  absorptive  powers  (Leslie's  Inquiry) 
1  being  the  absorptive  power  of  lampblack,  the  perpendicular  radiation 

of  a  lampblack  point  will  be  =  which   is  the   very  same  expres- 

1 — a 

sion  we  have  obtained  for  the  total  heat  radiated  and  reflected  together, 
falling  on  D,  in  the  same  perpendicular  direction  from  the  metallic 
point  C. 

48 


E AD I ATI ON   AND  ABSORPTION. 

periment,  while  the  latter  is  only  deduced  from  a  theoretical 
investigation.  It  will  also  be  seen,  that  by  increasing  the 
thickness  of  the  radiating  plate  indefinitely,  the  radiation  be- 
comes ultimately  independent  of  the  diathermancy  of  the  plate 
and  is  regulated  only  by  its  refractive  index. 

34.  The  connection  which  we  have  attempted  to  trace  be- 
tween the  refractive   and  radiative  power  of  a  substance,  pre- 
sumes that  those  rays  which  we  have  been  considering,  have  the 
power  of  forming  wave  lengths  with  the  medium  under  con- 
sideration ;  that  is,  of  being  capable  of  proper  reflection  and 
refraction. 

It  may  be,  however,  that  glass  and  other  similar  substances 
are  so  opaque,  with  respect  to  most  of  the  rays  of  heat  of  low 
temperature,  as  to  stop  them  almost  entirely  at  the  surface. 

As  such  rays  may,  therefore,  be  conceived  to  be  absorbed 
within  the  limit  of  physical  surface  of  the  medium,  the  cor- 
responding radiation  may  be  conceived  to  proceed  from  this 
physical  surface.  To  such  a  case  we  may  perhaps  suppose  reason- 
ing similar  to  that  of  Fourier  (as  given  by  Professor  Forbes 
in  the  Philosophical  Magazine  for  Feb.,  1833,)  to  be  applicable  ; 
the  intensity  of  radiation  being  therefore  proportional  to  the 
sine  of  the  angle  which  the  direction  makes  with  the  surface. 

35.  Let  us  now  see,  in  conclusion,  whether  these  investiga- 
tions seern  to  point  out  any  connection  between  internal  radia- 
tion and  conduction. 

Now,  without  in  the  least  confirming  that  these  are  identical 
there  seern  to  be  two  points  of  similarity  between  them. 

1st,  Since  the  heat  which  enters  metals  is  all  absorbed  at  a 
very  small  depth,  it  follows  that  the  flux  of  radiant  heat  from 
within  upon  the  interior  of  metallic  surface  is  derived  from  a 
very  small  depth. 

Also,  if  we  allow  (what  it  has  been  endeavored  to  prove,  Art. 
30)  that  the  flux  of  heat  upon  the  interior  of  the  surface  is  pro- 
portional to  the  index  of  refraction,  this  flux  will  be  greatest  in 
the  case  of  metals  which  may  be  supposed  to  have  a  very  high 
refractive  power ;  besides  which,  it  will,  as  we  have  seen,  be 
derived  from  a  very  small  depth.  The  radiation  of  a  metallic 
particle  is  therefore  very  great. 

Now,  if  internal  radiation  be  in  nny  way  connected  with  con- 

49 


MEMOIRS  ON 

duction,  we  might  expect  that  good  conducting  substances 
should  also  be  good  internal  radiators  of  heat,  and  we  see  they 
are  so. 

2d,  The  second  bond  of  similarity  is  this.  It  seems  to  be  a 
law  that  substances  are  almost  invariably  more  diathermanous 
for  heat  of  high  temperature  than  for  heat  of  low  ;  consequently, 
at  high  temperatures,  the  radiation  of  a  thin  plate  or  particle 
of  a  substance  will  bear  a  smaller  proportion  to  the  total  lamp- 
black radiation  of  that  temperature  than  at  low  temperatures. 
The  internal  radiations  of  particles  of  bodies  would  therefore 
diminish  at  high  temperatures  (not  absolutely,  but  with  respect 
to  the  proportion  which  they  would  bear  to  the  total  radiation 
of  these  temperatures).  If  the  same  rule  holds  for  metals,  and 
'conduction  be  connected  with  internal  radiation,  we  should  ex- 
pect that  at  high  temperatures  the  conducting  power  of  metals 
would  be  less  than  at  low  temperatures.  Now  this  has  been 
proved  to  be  the  case  by  Professor  Forbes. 


50 


RESEARCHES  ON  RADIANT  HEAT. 

SECOND  SERIES. 

BY 

BALFOUR   STEWART. 

Transactions  of  the  Royal  Society  of  Edinburgh. 
Vol.  XXII,  PL  I.  pp.  59—73.     April,  1859. 


51 


CONTENTS. 


PAGE 

Division  of  Subject      .        \        .        .         .        .         .         ,:      53 

Instruments  used  and  Method  of  Investigation     .        .         .53 
Effect  of  Roughening  the  Surface  of  a  Body  upon  its  Radi- 
ation     .        .        .        .         .  .         .         .        .53 

Nature  of  the  Heat  Radiated  by  Rock  Salt          .         .        .56 
Radiation  of  Glass  and  Mica  at  high  Temperatures   ...      59 
On  the  Law  which  Connects  the  Radiation  of  a  Body  ivilh  its 

Temperature  .         .        .        .        .         .        .s        ..        .64 

On  General  Diathermancy    .        .         .         .         .         ,        .69 


52 


VI.— RESEARCHES  ON  RADIANT  HEAT. 

SECOND  SERIES. 

BY  BALFOUR  STEWART,  M.  A. 

COMMUNICATED  BY  PROFESSOR  FORBES. 

(Read  April  18th,  1859.) 

Division  of  Subject. 

1.  The  first  part  of  this  paper  describes  the  following  groups 
of  experiments  : 

Group  I.     On  the  effect  which  roughening  the  surface  of  a 

body  produces  on  its  radiation. 
II.     On  the  nature   of  that  heat  which  is   radiated  by 

rock  salt  at  212° F.  . 

III.     On  the  radiation  of   glass  and  mica,  at  high  tem- 
perature. 

The  second,  or  theoretical,  portion  of  the  paper,  has  refer- 
ence to  the  law  which  connects  the  radiation  of  a  particle  with 
its  temperature  and  to  Dulong  and  Petit's  experiments  on  this 
subject. 

There  is  also  an  addition  of  a  later  date  than  the  rest  of  the 
paper  on  General  Diathermancy. 

Instruments  used,  and  Method  of  Investigation. 

2.  The  instruments   used,  and  the  method  of  using  them, 
were  much  the  same  as  described  in  the  first  series  of  these  re- 
searches, Art.  3.     Should  any  difference  occur  in  the  method  of 
conducting  a  particular  experiment,  it  will  be  mentioned  when 
the  experiment  so  performed  comes  to  be  described. 

First  group  of  Experiments  Described. 

3.  This  group  of  experiments  has  reference  to  the  effect  of 
roughening  the  surface  of  a  body  upon  its  radiation.     This  was 

53 


MEMOIRS   ON 

suggested  to  the   writer  by  Professor  Forbes.     The  first  sub- 
stance tried  was  rock  salt. 

A.  Rock  salt. — It  was  found  that  roughening  the  surface  by 
means  of  emery  paper,  until  it  became  quite  dim,  had  little  or 
no  effect  in  increasing  the  radiation,  as  will  be  seen  from  the 
following  statement  embodying  the  mean  result  of  three  sets  of 
experiments.* 

The  pieces  used  were  the  middle  piece  (thickness  =.36  inch) 
and  the  thickest  piece  (thickness  =  -77  inch),  described  in  first 
series,  Art.  6.  These  pieces  were  placed  at  a  distance  of  about 
four  inches  from  the  mouth  of  the  polished  brass  cone,  and  in 
order  to  increase  the  effect,  no  diaphragm  was  used.  They 
were  heated  in  the  boiling-water  apparatus  already  described. 
With  this  arrangement 

The  thick  piece  gave,  when  polished,  a  deviation  of  .21°.! 

when  roughened,    21.8 

The  middle  piece  gave,  when  polished,  a  deviation  of  .13.6 
when  roughened, 13.5 

4.  The  next  point  was  to  ascertain  if  roughening  had  any 
effect  upon  the  quality  of  heat  radiated. 

The  following  table  will  show  that  it  does  not  alter  the  qual- 
ity of  the  heat  sensibly;  its  quality  being  tested  by  its  capacity 
of  penetrating  a  screen  of  rock  salt. 

TABLE  I. 


SOURCE  OF  HEAT. 

Percentage    of    whole 

Heat 

which    penetrates    a  Rock 
Salt    Screen   thickness     .29 

inch. 

Rock  salt, 

.77  inch  thick, 

49 

51 

Rock  salt, 

.36  inch  thick, 

42 

roughened,  

43 

*In  the  experiments  with  roughened  surfaces,  only  one  of  the  sur- 
faces of  the  substance  was  roughened,  the  other  being  left  polished. 
In  radiation  experiments,  therefore,  the  roughened  surface  was  placed 
next  the  pile;  while  in  transmission  experiments  it  was  placed  furthest 
from  the  pile. 

54 


RADIATION  AND   ABSORPTION. 

The  trifling  difference  between  polished  and  roughened  salt 
in  this  table  may  fairly  be  attributed  to  error  of  experiment. 
We  may  therefore  conclude,  that  roughening  by  emery  paper 
neither  alters  the  quantity  nor  the  quality  of  the  heat  radiated 
by  rock  salt. 

5.  Again,  the  transmissive  power  of  rock  salt  for  lampblack 
heat  of  the  temperature  212°,  is  not  sensibly  altered  by  rough- 
ening the  surface.     This  will  be  seen  from  the  following  state- 
ment : 

The  percentage  of  Lampblack 

heat  transmitted  was 
With  Screen  of  Rock  salt,  thick- 
ness .36  inch,  polished, 77 

With  Screen  of  Rock  salt,  thick-    * 

ness  .36  inch,  roughened, 77 

This  result  naturally  follows  from  the  previous  one,  for  it 
has  been  shown  (First  Series,  Art.  19)  that  the  absorption  of  a 
plate  equals  its  radiation  and  since  roughening  its  surface  does 
not  influence  the  radiation  it  ought  not  to  influence  the  absorp- 
tion. 

6.  B.     Glass. — It  is  already  known   that   roughening   the 
surface  of  a  plate  of  glass  does  not  sensibly  increase  its  radia- 
tion.    It   is   only  necessary,  therefore,    to   ascertain   whether 
roughening   the  surface  of  a  radiating  plate  of  glass  alters  the 
capacity  of  its  heat  for  penetrating  a  screen  of  glass.     Accord- 
ingly, a  plate  of  crown  glass  .05  inch  thick,  3.75  inches   square 
being  placed  before  the  cone  as  a  screen,  and  a  similar  plate 
roughened,  heated  in  the  boiling-water  apparatus,  being  used 
as  the  source  of  heat,  and  no  diaphragm  used, 

The  deviation  was 1°.0 

When  the  source  of  heat  was  a  similar  plate,  .10  inch 

thick,  the  deviation  became, 1.5 

And  lastly,  when  the  source  of   heat  was   a   plate 

covered  with  lampblack,  the  deviation  was, 1.9 

With  the  same  sources  of  heat,  only  the  glass  polished  in- 
stead of  being  roughened,  these  numbers  were  0°.95,  1°.45, 
1°.95.  From  the  correspondence  between  these  two  sets  of  re- 
sults, we  may  infer  that  the  quality  of  the  heat  radiated  by 
glass  (at  least  in  so  far  as  transmission  through  a  plate  of  glass 

55 


MEMOIRS     ON 

can  test  it)  is  not  altered   by  roughening  the   surface  of  the 
glass. 

7.  And  from  all  these  experiments,  we  may  infer  (what  has 
indeed    been   already   remarked   by   Professor   Forbes),    that 
although  roughening  its  surface  with  sand  or  emery  paper  ren- 
ders a  body  dim  for  light  yet  it  still  remains  specular  for  heat 
rays,  which,    possessing  a  greater  wave  length  than  those  of 
light,  are  less  liable  than  the  latter  to  be  influenced  by  scratches 
or  furrows. 

Second  Group  of  Experiments  Described. 

8.  The    second    group   of    experiments    has   reference   to 
the  nature  of  the  heat  which  is  radiated  by  rock  salt  at  212°. 
Its  quality  being  tested  by  transmission  through 

a.     A  screen  of  mica. 

/?.     One  of  mica  split  by  heat. 

7.     One  of  glass. 

9.  a.     Mica  Screen. — By  the  mean  of  three  sets  of  experi- 
ments, a  mica   screen   (thickness  =  .003  inch  nearly)   passed 
about  31  per  cent  of   ordinary  lampblack   heat,   while  it  only 
passed  18  percent  of  rock  salt  heat.     Or  if  we  call  the  proportion 
of  black  heat  passed  by  the  mica  100,  that  .of  rock  salt  heat  will 
be  58. 

10.  /5.     Split  Mica  Screen. — Two  sets  of  experiments  agreed 
in  giving  twenty  per  cent  as  the  proportions  of  lampblack  heat 
of  212°,  transmitted  through  a  screen  of  mica  split  by  heat, 
while  the  proportion  of  rock  salt  heat  transmitted  by  the  same 
screen  was    only  15^   per  cent.     These  numbers  are   to   one 
another  as  100  to  76. 

11.  y.     Glass  Screen. — In  order  to  avoid  secondary  radiation 
from   the  screen,  which,  in  this  case,  absorbs  nearly  all  the 
heat,  two  screens  of   microscopic  glass   were  used,  the  one  be- 
hind the  other,  with  an  interval  between. 

Moreover,  as  in  this  case,  the  proportion  of  heat  transmitted 
is  exceedingly  small,  the  following  arrangement  was  adopted  to 
make  it  measurable. 

The  experiment  consisted  of  four  parts, 

1st.  The  effect  of  rock  salt  heat  upon  the  pile  without  a 
screen  was  observed  by  the  ordinary  galvanometer. 

56 


RADIATION  AND   ABSORPTION. 

2d.  The  effect  of  lampblack  heat,  also  without  a  screen, 
was  observed  by  the  same  galvanometer. 

3d.  The  wires  of  the  pile  were  then  transferred  to  a  more 
sensitive  galvanometer,  and  the  effect  of  lampblack  heat 
observed,  the  glass  screen  being  interposed. 

4th.  The  sensitive  galvanometer  and  glass  screen  being  re- 
tained, the  effect  of  rock  salt  heat  was  lastly  observed. 

By  this  method  of  experimenting,  it  was  merely  the  relation 
between  the  diathermancy  of  the  screen  for  lampblack  heat 
and  for  rock  salt  heat  that  was  measured;  its  absolute  diather- 
mancy for  either  of  these  heats  not  being  determined.  Two 
sets  of  experiments,  conducted  in  this  manner,  gave  the  fol- 
lowing result: 

By  the  first  set,  calling  the  proportion  of  the  whole  lamp- 
black heat  which  passed  the  screen  100,  that  of  the  rock  salt 
heat  which  passed  the  same  screen  was  54.  And  by  the  second 
set,  these  numbers  were  100  to  60. 

12.  As  in  these  experiments  with  a  glass  screen  the  propor- 
tion of   heat  passed    is  very  small,    great  numerical  accuracy 
cannot   be   looked  for  and   the  results   obtained  are  valuable 
rather  as  determining   the  direction  and  character  of  a  fact, 
than  as  measuring  the  extent  to  which  it  holds. 

13.  It  is  already  well  known  that  rays  of  great  ref  rangibility 
or  small  wave  length  pass  through  glass  and  rnica  more  readily 
than   those   of   an   opposite   character.     The    difficulty   with 
which  rock  salt  heat  penetrates  these  substances  as  compared 
with  ordinary  heat  might  therefore  lead  us  to  infer  that  the 
wave  length  of  this  heat  is  greater  than  that  of  ordinary  lamp- 
black heat. 

14.  If,  therefore,  the  heat  radiated  by  rock  salt  is  of  great 
wave  length  since  (First   Series,    Art.    19)  'the  quality  of  the 
heat  radiated  is  the  same  as  that  of  the  heat  absorbed,  it  follows 
that  the  heat  most  absorbed  by  rock  salt  must  be  heat  of  great 
wave  length;  and  this  derives  confirmation  from  a  fact  noticed 
by  Professor  Forbes,  viz.,   that  rock  salt   passes   a   somewhat 
greater  proportion  of  heat  of  high  temperature  than  of  that  of 
low;  heat  of  high  temperature  possessing  a  less  average  wave 
length. 

15.  If  we  look  now  to  the  relative  transmission  of  the  two 

57 


MEMOIES     ON 


descriptions  of  heat  through  mica  split  by  heat,  we  see  that 
the  facility  of  transmission  is  yet  in  favor  of  ordinary  heat,  but 
not  so  strikingly  as  with  a  screen  of  common  mica.  This  will 
be  seen  from  the  following  table  : 

TABLE  II. 


NATURE  OF  SOURCE. 

Transmission   of    Or- 
dinary Heat,  at 
212°  F. 

Transmission  of 
Rock  salt  Heat 
at  212°  F. 

Mica  

100 

58 

Mica  split  by  heat  

100 

76 

Compare  this  with  the  following  table  deduced  from  the 
results  given  by  Professor  Forbes,  in  the  Fourth  Series  of  his 
Researches,  Art.  9. 

TABLE  III. 


NATURE  OF  SCREEN. 

Transmission   of   Heat 
from  Blackened  Brass 
at  700  °  F. 

Transmission   of 
Black  Heat 
at  212°  F. 

iSlica  015  incli  thick 

100 

52 

100 

64 

From  a  comparison  of  these  two  tables,  it  will  be  seen  that, 
as  tested  by  the  two  substances,  mica  and  mica  split  by  heat, 
rock  salt  heat  at  212°  F  bears  to  ordinary  heat  of  that  temper- 
ature a  relation  similar  to  that  which  ordinary  heat  at  212°  F 
bears  to  heat  at  700°  F;  that  is  to  say,  that  just  as  heat  of  212° 
F  has  a  greater  wave  length  than  heat  of  700°  F,  so  rock  salt 
heat  at  212°  F  has  a  greater  wave  length  than  ordinary  heat  at 
that  temperature.  And  the  surface  stoppage  produced  by 
splitting  the  mica,*  telling  most  powerfully  upon  heat  of  high 
temperature,  or  small  wave  length,  while  the  stoppage  by  sub- 
stance is  in  the  opposite  direction,  we  see  how  the  one  effect 
tends,  to  a  certain  extent,  to  neutralize  the  other,  rendering  the 
proportions  of  different  kinds  of  heat  passed  by  split  mica  more 
nearly  alike  than  those  passed  by  ordinary  mica. 

16.  All  these  experiments  concur  in  showing  that  heat  from 
rock  salt  possesses  very  great  wave  length,  and  probably  heat 
from  a  thin  plate  of  this  substance,  at  a  low  temperature,  may 

58 


HAD  I  ATI ON   AND    ABSORPTION. 


C,E 


be  found  to  possess   a  greater  average  wave  length  than  any 
other  description  of  heat  which  can  be  exhibited. 

Third  Group  of  Experiments  Described. 

17.  I  now  proceed  to  describe  the  third  group  of  experiments, 
or  those  on  the  radiation  of  glass  and  mica  at  high  tempera- 
tures. 

A.  Glass. — For  the  experiments  on  glass,  the  following 
apparatus  was  used:  The  pile  was  placed  within  a  box,  and 
surrounded  with  cotton  wadding.  The  orifice  through  which 
radiant  heat  was  admitted  into  the  box  consisted  of  a  brass 
tube  AB,  blackened  in  the 
inside.  The  diameter  of  this 
tube  was  £  inch,  its  length  3 
inches,  and  during  the 
greater  part  of  its  length  it 
passed  through  water,  con- 
tained in  the  chamber  CEFD.  The  side  of  the  box  (CAD)  next 
the  pile  was  lined  with  tin  foil.  Owing  tothesmall  divergence 
of  the  rays  of  heat  which  hud  to  pass  through  the  narrow  tube, 
the  cone  might  be  placed  several  inches  to  the  left  of  A  without 
sensibly  weakening  the  effect,  and,  on  the  other  hand,  the 
source  of  heat  might  be  placed  some  distance  to  the  right  of  D 
without  ceasing  to  fill  up  the  field  of  view.  By  this  means,  the 
distance  between  the  pile  and  the  source  of  heat  being  consider- 
able, no  currents  of  heated  air  from  the  latter  would  be  able  to 
reach  the  former;  and  as  the  tube  AB  was  blackened  in  the  in- 
side, and  passed  through  water,  reflection  and  secondary  radia- 
tion would  both  be  avoided.  By  means  of  a  lid  fitting  on  the 
tube  at  A  the  aperture  might  be  diminished  at  pleasure.  The 
pile  was  connected  with  a  very  sensitive  galvanometer. 

When  glass  at  a  high  temperature  was  the  source  of  heat, 
a  very  small  aperture  was  sufficient,  and  thus  the  advantage  was 
gained  of  having  the  whole  field  covered  with  glass,  all  at  a 
high  temperature,  which  could  not  have  been  the  case  had  the 
aperture  been  large. 

Slips  of  glass  about  £  inch  broad  were  used,  and  were  set  ver- 
tically, just  touching  a  gas  flame  from  a  Bunsen's  burner. 
When  two  slips — one  behind  the  other — were  used,  the  one 

59 


MEMOIRS     ON 

just  touched  that  portion  of  the  flame  next  the  pile,  and  the 
other  that  portion  furthest  from  it.  A  cross  section  of  the 
arrangement  is  shown  on  page  59. 

A  single  slip  of  glass  about  .1  inch  thick  thus  heated  gave  a 
deviation  of  16°. 5,  while  two  slips,  the  one  behind  the  other, 
gave  18°. 5.  When  the  slips  were  .05  inch  thick  these  numbers 
were  29 M  and36°.3. 

18.  From  these  experiments  we   may   conclude,  that   at   a 
high  temperature,  700°    or   800°    F,    the   radiation   from   two 
plates  of  glass,  one  behind  the   other,  is   sensibly  greater  than 
that  from  one — a  result  which  does  not  hold  for  glass  at  212°. 
Or  the  fact  may  be  stated  thus: 

The  radiation  of  a  single  plate  of  glass  bears  a  smaller  pro- 
portion to  the  total  radiation  of  700°  than  at  212°. 

19.  It  was  next  tried  whether  the  capacity  of  a  glass  screen 
for  passing  heat  from  blackened  copper  at  700°   was  altered  by 
its  being  heated. 

In  order  to  ascertain  this,  blackened  copper  at  700  °  F  was 
placed  behind  a  slip  of  glass,  and  the  amount  of  heat  from  the 
copper  which  passed  the  glass  was  observed. 

Firstly,  When  the  glass  was  cold. 

Secondly,  When  it  was  heated  to  between  700°  and  800°  F. 

20.  As  in  these  experiments   the  considerably   fluctuating 
temperature   of    the  source  of   heat  causes  a  somewhat  large 
difference  between  successive  observation,  and  renders  necessary 
a  great  number  in  order  to   arrive   at   a  correct  result,  it  was 
thought  desirable,  instead  of   using  momentary  deviations,  to 
employ  permanent  ones.     This  was  done  with  complete  success; 
the  application  of  the  heated  copper,  or  its  removal,  causing  an 
unmistakable  alteration  of  the  position  of  the  needle. 

21.  The  experiment  was  then  varied  in  the  following   man- 
ner:    The  needle  was  kept  permanently  deviated  by  the  heated 
glass,  and  the  momentary  swing  due  to  the  application  or  with- 
drawal of  the  heated  copper   was   noticed,  and  was  compared 
with  that  occasioned  by  the  hot  copper  when  the  glass  was  cold 
and  the  needle  at  zero. 

22.  These  experiments,  which  are  not,  perhaps,  individually 
susceptible  of  very  great  exactness,  agreed,  however,  in  render- 
ing  it   probable   that  glass,  owing  to  its  being  heated  up  to 

60 


RADIATION  AND  ABSORPTION. 

about  700°  F.   does   not   change  its   diathermancy  for  heat  of 
700°  F. 

23.  B.     Mica. — The  experiments  on   mica  were  made  with 
the  ordinary  galvanometer.     A  piece  of    mica,  thickness  about 
.008  of  an  inch,  being  used  as  a  screen,  and  a  diaphragm,  .65  of 
an  inch  square,  at  the  distance  of  three  inches  from  the  mouth 
of  the  pile,  being  employed,  the  mean  of  two  sets  of  experiments 
made  the  proportion  of  black  heat   of  200°   F  passed  by  the 
mica  to  be  13  per  cent.     Placing  an  additional  diaphragm  of 
the  same  size  3|  inches  beyond  the  first,  and  using  as  a  source  the 
temperature  of  400°   F,  the  mean  of  two  sets  of  experiments 
made  the  proportion  of  heat  passed  by  the  mica  screen  to  be  21 
per  cent. 

In  order  to  test  whether  the  apparently  greater  diathermancy 
of  the  screen  for  heat  of  400°  F  was  owing  to  the  difference  in 
the  nature  of  the  heat,  or  to  the  heat  at  400°  F  striking  the 
screen  more  nearly  at  a  perpendicular  incidence,  and  thus 
experiencing  less  reflection  as  well  as  passing  through  a  smaller 
thickness  of  mica,  an  experiment  was  made  on  heat  at  200°  F, 
with  the  arrangement  and  distance  used  for  heat  of  400  °  F, 
which  seemed  to  show  that  this  difference  of  distance  does  not 
affect  sensibly  the  proportion  transmitted.  We  may  therefore 
conclude  that  the  difference  in  proportions  transmitted  is  ow- 
ing to  a  difference  of  quality  in  the  two  descriptions  of  heat. 

24.  A  cast-iron  box  was  next  constructed  having  this  same 
plate  of  mica  inserted  as  a  window,  so  that,  while  one  side  of 
the  box  consisted  merely  of  a  moderately  thin  plate  of  cast- 
iron,  the  other,  except  round  the  edges,  was  composed  of  mica. 
The  cast-iron  side  was  then  blackened,  and  the  box  filled  with 
mercury.     A  thermometer  inserted   in  the   box  measures  the 
temperature.     At  200°  F,  with  the  usual  diaphragm  three  inches 
from  the  mouth  of  the  pile,  the  proportion  between  the  radia- 
tion of  the  blackened  side  and  the  mica  window  was,  by  the 
mean  of   three  sets  of  experiments,  as   100  to   87.8,  while   at 
400°   F,  with  the  usual  arrangement  of  two  diaphragms,  the 
same  proportion  was  100  :  84.1. 

25.  Let  us  endeavor  to  discuss  these  results.     The  radiation 
from  the  mica  window  consists  of  three  portions  : 

a.     The  proper  radiation  of  the  mica  plate. 

61 


MEMOIRS    ON 

/?.  That  portion  of  the  radiation  of  the  mercury  which  has 
been  able  to  penetrate  the  mica  plate. 

y.  That  portion  of  the  radiation  of  the  mica  which,  strik- 
ing upon  the  mercury,  is  reflected  back  by  it  and  has  pene- 
trated the  mica  plate. 

Now,  supposing  there  was  no  mercury  behind  the  mica,  and 
that  rnica  between  200°  and  400°  does  not  alter  its  diathermancy 
as  a  screen  in  any  respect,  let  us  inquire  what  ought  to  have 
been  the  result  obtained.  Then,  since  the  radiation  of  a  thin 
plate  equals  its  absorption  (First  Series,  Art.  19),  and  since 
the  absorption  of  this  mica  plate  was  8  per  cent  less  at  400° 
than  at  200°  (Art.  23),  its  proportional  radiation  ought  to  be 
8  per  cent  less  at  400°  than  at  200°. 

26.  But  the  effect  of  the  mercury  behind  the  mica  mani- 
festly tends   to  diminish   this  difference.     For   we  know  that 
the  mica  (Art.  23)  passes  8  per  cent  more  of  lampblack  heat  at 
400°  than  at  200° ;  it  will  therefore  no  doubt  pass  a  greater  pro- 
portion of  the  heat  from   the  mercury  behind  at  400°  than  at 
200°.     But  we  have  reason  to  think  that  the  radiation  of  mer- 
cury  is   nearly   %'  of   that   of   lampblack.*     Consequently  we 
may  suppose  that  owing  to  this  action  of  the  mercury,  the  pro- 
portional  radiation  of  the  mica  window  at  400°   is  increased 
about  y±  of  8,  that  is,  2  percent.     This  reduces  therefore  the 
difference  from  8  to  6  per  cent. 

27.  But  the  mercury  acts   in  another  manner  also  in  the 
same    direction.     Had  mercury   been   a   perfect   reflector,    its 
presence  behind  the  mica  would  have  been  equivalent  to  doub- 
ling  the  thickness  of   the  plate  ;   for  it  would  have  sent  the 
whole  radiation  of  the  mica  that  fell  upon  it  back  through  the 
mica.     But  the  difference  between  the  proportional  radiation  at 
200°  and  at  400°  is  less  for  a  thick  plate  of  mica  than  for  a  thin 
one  (indeed,  when  the  plate  is  indefinitely  thick,  this  difference 
vanishes,  and  the  proportional  radiation  is  the  same  at  all  tem- 
peratures); this  action  of  the  mercury,  therefore,  would  tend 
still  further  to  diminish  the  already  diminished  difference  of 

*  Provostaye  and  Desains  estimated  the  proportion  of  heat  reflected 
by  mercury  to  be  77  per  cent.  The  radiation,  being  complementary  to 
this,  may  be  reckoned  to  be  23  per  cent  nearly. 

62 


RADIATION  AND  ABSORPTION. 

6  per  cent.  The  amount  of  this  action  cannot  be  far  from 
3  per  cent,  *  in  which  case  the  6  per  cent  would  be  reduced 
to  4  per  cent ;  now  3.7,  or,  in  round  numbers,  4  per  cent  is  the 
observed  difference  between  the  proportional  radiation  of  the 
mica  window  at  the  temperatures  200°  and  400°. 

28.  We  see  thus  that  the  behavior  of  the  mica  as  a  screen, 
compared  with  its  behavior  as  a  radiator,  agrees  very  well  with 
the  supposition  which  we  made  in  Art.  25;  viz.,  the  mica  between 
the  temperatures  of  200°  and  400°  does   not  alter  its   diather- 
mancy in  any  respect;  a  result   similar  to  that  which  we  have 
already  deduced   for  glass   (Art.  22)    between  somewhat  wider 
limits. 

29.  Experiments  with   the   same   object  in   view,  but  of  a 
more  direct  description,  were  made  upon  mica,  similar  to  those 
already  described  as   having  been   made  upon   glass,  that  is,  it 
was  endeavored  to  ascertain  whether  hot    mica  passed  as    much 
heat  from  hot  copper  as   cold  mica;  but   in  these  experiments 
the  fluctuation  was   very  considerable,  probably   owing   to  the 
small   body  of  the   mica.     Nevertheless,    they  confirmed  the 
results   above   obtained  ;   viz.,  that  mica  does  not   change   its 
diathermancy  in  any  respect  owing  to  its  being  heated. 

30.  We  may  therefore  conclude  that  this  property   (at  least 
within  moderate  limits)  is  common  both  to  glass   and  to   mica, 
and  indeed,  a  priori,  there  appears  no  good  reason  why  the  mere 
heating  of  a  substance  should  change  its   diathermancy.     It  is 
the  theoretical  importance  of  this  property  that  has  induced  me 
to  take  pains  to  verify  experimentally  and  its  importance  will 
be  seen  from  some  of  the  consequences  which  follow  its  estab- 
lishment, which  I  shall  now  proceed  to  discuss. 

*  It  would  have  been  better  to  have  tested,  by  means  of  a  direct  exper- 
iment, to  what  extent  the  difference  between  the  proportional  absorp- 
tion and  radiation  of  mica  at  200°  F  and  at  400°  F  would  have  been 
diminished  by  doubling  the  thickness  of  the  plate;  but  unfortunately 
the  plate  of  mica  was  so  much  cut  up  by  being  used  as  a  window,  as  to 
be  unfit  for  being  formed  into  a  double  screen. 

We  see,  however,  from  Art.  37,  that  while  the  difference  between  the 
proportional  radiation  of  a  plate  of  glass  (thickness  imm)  at  100°  C  and 
and  390°  C  is  9  per  cent,  the  same  difference  for  a  plate  of  double  the 
thickness  is  only  7  per  cent,  or  2  per  cent  less.  We  may,  therefore,  with- 
out much  risk  of  error,  adopt  this  difference  of  2  per  cent  for  mica  un- 
der experiment. 

63 


MEMOIRS     ON 

On  the  Law  ivhich  Connects  the  Radiation  of  a  Body  with  its 
Temperature. 

31.  The  experiments  of  Dulong  and  Petit  upon  the  cooling  of 
two  thermometers,  one  naked,  and  the  other  covered  with  silver, 
seemed  to  show  that  the  proportion  between   the   radiations  of 
these  two  substances  was  the  same  at  the  different  temperatures 
of  experiment. 

Now  I  have  endeavored  to  prove  in  these  researches — 1st, 
That  the  radiation  of  a  thin  plate  at  any  temperature  equals  its 
absorption  of  black  heat  of  that  temperature.  2nd,  That  the 
diathermancy  of  glass  and  mica  (and  probably  of  other 
substances)  is  not  altered  by  heating  the  substances.  Again,  it 
is  well  known  that  substances  are  generally  more  diathermanous 
for  heat  of  high,  than  for  heat  of  low  temperature;  it  follows 
that  the  radiation  of  a  thin  plate  of  a  substance  at  a  high 
temperature  should  bear  a  less  proportion  to  the  total  radiation 
of  that  temperature  than  at  a  low  temperature. 

32.  While,   therefore,  it  is   likely  that  the   radiation   of   a 
silvered   thermometer  (silver  leaf  being  quite   opaque   for  all 
heat)    will  bear  a   constant  relation  to    that    of  a  blackened 
thermometer  at  all  temperatures,  we  should  expect  that  for  a 
naked    thermometer,  just  as  for  the  mica   window,  the  radia- 
tion should  bear  a  somewhat  less  proportion  to  the  total  radia- 
tion at  a  high  temperature  than  at  a  low.     We  should  therefore 
expect  the  radiation   of   the  naked   thermometer  to   increase 
somewhat  less  rapidly  with  the  temperature  than  that  of  the 
silvered      thermometer.     Dulong      and     Petit,     nevertheless, 
found  the  rate  of  increase  to  be  the  same  for  both. 

33.  Now,    in   the   first    place,  since    glass   is    exceedingly 
opaque  for  heat  even   of  300° C  (the  highest  temperature  ex- 
perimented on),  the  difference   we  are  in  search  of  (analogous 
to  the  diiference  of  four  per  cent  in  the  mica  window)  would 
be  exceedingly  small.     But,  in  the  second  place,  Dulong  and 
Petit  had  two  thermometers,  one  of  which,  containing  about 
three  pounds  of  mercury,  was  used  for  high,  and  the  other  and 
smaller   one  for  low  temperatures.     This  latter    circumstance 
will  complicate  or  even  vitiate  their   experiments  so  far  as  re- 
gards this  peculiar  difference  we  are  treating  of. 

64 


RADIATION  AND   ABSORPTION. 


34.  Although,  for  these  reasons,  attaching  little  importance 
to  Dulong's  and  Petit's  observations,  so  far  as  varying  diather- 
mancy is  concerned,  yet  it  may  be  well  to  state  that  they  show,  on 
the  whole,  a  very  small  difference  in  the  direction  which  would 
indicate  a  superior  diathermancy  of  the  glass  at  a  high  tempera- 
ture. 

35.  Assuming  it  proved  that  the  proportional  radiation  of  a 
thin  plate  is  less  at  a  high  than  at  a  low  temperature,  I   shall 
now   endeavor  to   show  that   this    difference   increases   as   we 
diminish  the  thickness  of  the  plate.     To  prove  this,  it  is  only 
necessary  to  exhibit  the  following  table,  given  by  Melloni  : 

TABLE  IV. 


NUMBER  OF  RAYS  OUT  OF  100  PASSED. 

Thickness  of 
Glass  Screen. 

Locatelli 
Lamp. 

Incandes- 
cent 
Platinum. 

Black 
Copper 
at  390  °  C. 

Blackened 
Copper 
at  100  °  C. 

mm 

0.07 

77 

57 

34 

12 

.5 

54 

37 

12 

1 

1.0 

46 

31 

9 

0 

2 

41 

25 

7 

0 

4 

37 

20 

5 

0 

6 

35 

18 

4 

0 

8 

33.5 

17 

3.4 

0 

36.  We  have  already  seen   that  glass   does  not  change   its 
properties  with  regard  to  heat,  by  being  raised  to  the  tempera- 
ture of  390  °C  ;  it  is  perhaps,  however,  too  much  to  conclude, 
that  when  heated   to  the  temperature  of   a  Locatelli  lamp,  its 
properties  would  remain  unchanged.     At  all  events,  in  order  to 
make  use  of  the  whole  of  the  above  table,  we  may   suppose  the 
properties  of   the  glass  to   remain   the   same   throughout,  es- 
pecially as  the  results  we  shall  deduce  from  the   supposition 
will  be  of  the  same  nature  as  if  we  had  only  extended  it  to  glass 
at  390°  C. 

37.  Presuming,  therefore,  that  the  diathermancy  of  glass  does 
not  alter  through  its  being  heated,  and  allowing  4  per  cent  as 
the  proportion  of  the  heat  striking  it  reflected  from  the  first 
surface  of  a  glass  screen,  and  supposing  also  the  same  propor- 
tion of  the  heat  which  is  able  to  reach  the  second  surface  to  be 

65 


MEMOIRS     ON 

reflected  from  it,  we  may,  on  the  principle  that  the  propor- 
tional radiation  of  a  plate  equals  its  proportional  absorption,  con- 
struct the  following  table  : 

TABLE  V. 


PROPORTIONAL  RADIATION  OF  GLASS  PLATES  AT  DIFFERENT 

TEMPERATURES,  (RADIATION  OF  LAMPBLACK  =  100), 

Thickness  of 
plate. 

Temp,  of  Lo- 
catelli  Lamp. 

Temp,  of  lu- 
candescent 
Platinum. 

3900  C> 

100°  C. 

mm 
0.07 

16 

37 

61 

84 

.5 

40 

58 

84 

95 

1.0 

48 

64 

87 

96 

2 

53 

70 

89 

96 

4 

58 

75 

91 

.96 

6 

60 

77 

92 

96 

8 

61.5 

78 

92.6 

96 

38.     Let  us  call  the  proportional  radiation  of  the  glass  plate 
at  100 °C  unity,  and  we  derive  the  following  table. 

TABLE  VI. 


PROPORTIONAL  RADIATION  OF  GLASS  PLATES  AT  DIFFERENT 
TEMPERATURES,  THEIR  RESPECTIVE  PROPORTIONAL  RADI- 
ATIONS AT  100  C.  BEING  RECKONED  UNITY. 

Thickness  of 
Plate. 

100°  C. 

390°  C. 

Temp,  of  In- 
candescent 
Platinum. 

Temp,  of  Lo- 
catelli  Lamp. 

mm 
0.07 
.5 
1.0 
2 
4 
6 
8 

1 
1 
1 
1 
1 
1 
1 

.72 
.88 
.91 
.93 
.95 
.96 
.965 

.44 
.61 
.66 
.73 

.78 
.80 
.81 

.19 
.42 
.50 
.55 
.60 
.62 
.64 

39.  We  see  thus  that  the  radiation  of  thick  plates  of  glass  in- 
creases most  rapidly,  and  that  of  thin  plates  least  rapidly,  as  the 
temperature  increases,  and  we  may  suppose,  that  if  we  could 
procure  a  plate  of  glass  of  sufficient  tenuity,  we  might  (without 
heating  the  plate  at  all),  by  finding  its  absorption  for  heat  of 

66 


RADIATION   AND  ABSORPTION. 

different  temperatures  find  its  radiation  at  those  temperatures, 
which  (if  the  plate  were  thin  enough)  would  give  us  the  law  of 
radiation  of  a  glass  particle.  This  law  would  not  increase  nearly 
so  fast  with  increasing  temperatures  asDulong  and  Petit's  law  ; 
it  may  even  be  that  the  radiation  of  glass  particles  is  propor- 
tional to  its  absolute  temperature. 

40.  But  all  substances   (with  the   exception  of  black  mica 
and  black  glass,  whose  peculiarity  may  perhaps  be  otherwise  ex- 
plained) have  the  same  properties  as  glass  with  regard  to  heat ; 
that  is,  they  are  more  diathermanous  for  heat  of  high  than  for 
heat  of  low  temperatures.     The  radiation  of  thin    plates   or 
particles  of  all  substances  will   therefore  increase   less  rapidly 
with  temperature  than  that  of  black  surfaces.     It  may  there- 
fore be,  that  the  same  law  of  radiation  is  common  to  very  thin 
plates  or  particles  of  all  bodies  ;  this  law  (whatever  it  be)  giving 
in  all  cases,  a  less  rapid  increase  of  radiation  with  temperature 
than  is  indicated  by  Dulong   and  Petit's  law.     Had,  however, 
the  diathermancy  of  thin  plates  of  different  substances  in  some 
cases  diminished   and   in   others   increased   for  heat   of  high 
temperature,  the  law  of  radiation  of  a  particle  could  not  have 
been  the  same  for  all  bodies. 

The  generality  of  this  law  of  increased  diathermancy  of  all 
bodies  for  heat  of  high  temperatures  seems,  therefore,  to  me, 
to  argue  in  favor  of  the  universality  of  the  unknown  law  of 
particle  radiation  which  depends  upon  the  former. 

41.  What,  then,    does    Dulong   and   Petit's   law   express  ? 
The  answer  is,  it  expresses  the  law  of  radiation  of  indefinitely 
thick  plates,  and  we  have  shown  that  it  increases  faster  than 
the  law  of  radiation  of  a  material  particle. 

To  facilitate  the  comprehension  of  this  subject  as  much  as 
possible,  I  have  put  it  in  the  following  shape.  Suppose  we 
have  two  substances  opposite  one  another,  the  one  having  the 
temperature  of  0°,  and  the  other  of  100°,  the  latter  will  of 
course  lose  heat  to  the  former — let  us  call  its  velocity  100. 
Suppose,  now,  that  (the  first  surface  still  retaining  its  tempera- 
ture of  0°)  the  second  has  acquired  the  temperature  of  400°  ; 
then  we  should  naturally  expect  the  velocity  of  cooling  to  be 
denoted  by  400  ;  but  by  Dulong  and  Petit's  law,  it  is  much 
greater.  The  reason  of  the  increase  may  be  thus  explained. 

67 


MEMOIRS     ON 

At  the  temperature  of  100°  we  may  suppose  that  only  the  ex- 
terior row  of  particles  of  the  body  supplied  the  radiation,  the 
heat  from  the  interior  particles  being  all  stopped  by  the  ex- 
terior ones  as  the  substance  is  very  opaque  for  heat  of  100°  ; 
while  at  400°  we  may  imagine  that  part  of  the  heat  from  the 
exterior  particles  is  allowed  to  pass,  thereby  swelling  up  the 
total  radiation  to  that  which  it  is  by  Dtilong  and  Petit's  law. 

42.  We  have  thus  ascertained — 1st,  That  Dulong  and 
Petit's  law  is  not  the  law  of  radiation  of  a  material  particle  ; 
and,  2d,  That  this  law  increases  less  rapidly  with  the  tempera- 
ture than  Dulong  and  Petit's  law.  But  now  the  question  arises, 
can  any  method  be  indicated  of  ascertaining,  experimentally 
the  law  of  radiation  of  a  material  particle  ?  Now,  by  con- 
tinually diminishing  the  thickness  of  the  plate  whose  radiation 
at  different  temperatures  we  are  ascertaining,  we  certainly  ap- 
proach nearer  and  nearer  to  the  desired  law,  and,  by  using  the 
method  indicated  in  Art.  37,  we  may  avoid  heating  this  plate 
at  all  and  thus  overcome  one  source  of  experimental  difficulty. 
Yet  the  thinnest  plate  we  can  procure  of  a  substance  such  as 
glass  or  mica  acts,  to  all  intents,  as  an  indefinitely  thick  sub- 
stance for  a  great  many  of  the  rays  of  heat — that  is,  it  stops 
them  all.  The  change,  therefore,  of  the  unknown  law  of  par- 
ticle radiation  into  Dulong  and  Petit's  law  will  to  a  great 
extent,  have  taken  place  even  within  this  very  thin  plate  ;  so 
that,  in  order  to  reach  the  desired  law  or  even  approximate  to 
it,  we  should  have  to  use  much  thinner  plates  than  we  could  pos- 
sibly procure  ;  and,  even  without  the  necessity  of  heating  the 
films,  the  experimental  difficulty  and  labor  of  such  an  investi- 
gation would  be  very  great. 

On  the  other  hand,  we  may  suppose  that,  since  a  thin  film 
stops  so  much  heat,  a  portion  may  be  stopped  in  the  physical 
surface  of  the  body,  and  the  absorption  might  thus  influence 
the  law  of  reflection  of  heat  from  the  surface.  The  amount 
of  this  influence  depending  on  the  absorptive  nature  of 
the  particles,  we  might  be  able  to  measure  the  absorption,  and, 
consequently,  the  radiation  of  the  physical  surface,  that  is,  of 
a  very  thin  plate.  But,  in  the  first  place,  the  difficulties  of 
such  an  investigation  would  be  even  greater  than  in  the  previ- 

08 


E  A  D  I  A  T  I  0  N  A  N  D  A  B  S  0  R  P  T I  0  N  . 

ous  case  ;  and,  in  the  second  place,  the  true  law  of  reflection  is 
not  yet  finally  settled. 

I  am  therefore  induced  to  think  that  it  is  nearly  hopeless  to 
attempt  to  ascertain  the  true  law  of  radiation  of  a  material 
particle,  at  least  by  any  method  of  experimenting  depending 
upon  the  use  of  thin  plates,  or  on  the  change  which  absorption 
may  be  presumed  to  cause  in  the  amount  of  heat  reflected  from 
the  surface  of  a  body. 

Edinburgh,  March  22,  1859. 

On  General  Diathermancy   (added  15th  June). 

43.  Circumstances  having  occurred  which  may  interfere  in 
the  meantime  with  my  further  experiments  on  heat,  I  annex 
to  this  paper  an  account  of  some  experiments  made  since  the 
day  of  reading.     These  were  proposed  with   the  view  of  ascer- 
taining   whether    diathermancy   is    confined   to  rock  salt    or 
whether  bodies  partake  of  this  property.     If  the  latter  be  the 
case,  the  reason  why  we  have  not  hitherto  ascertained  it  to  be 
so  is  evidently  the  difficulty  of  obtaining  crystals  of  many  bodies 
sufficiently  large  to  operate  upon  ;  and  if  we  wish  to  prove  these 
diathermanous  we  must  do  so  in  a  way  that  does  not  render  nec- 
essary the  use  of  large  crystals. 

44.  Now,  a  body  that  is  transparent  for  light,  forms,  when 
pounded,  a  white  powder  or  one  that  reflects  a  great  deal  of 
light.     It  will  be  granted  that  the  reason  of  this  is  because  we 
have  not  only  the  reflection  from  the  outer  surfaces  of   the 
crystals,  but  also  from  many  interior  surfaces.     Now  the  same 
remark  is  applicable  to  heat.     A  body  that  is  diathermanous  or 
transparent  for  heat  should,  as  a  powder,  be  white  for  heat,  or, 
in  other  words,  reflect  it.     But  (First  Series,  Art.  31)  the  re- 
flection plus  the   radiation   of   the  body  at   any  temperature 
equals  the  lampblack  radiation  at  that  temperature.     Hence  a 
powdered  diathermanous  substance  ought   to  radiate  less  than 
lampblack.      Accordingly,    different    substances    having   been 
pounded  into  a  fine  crystalline  powder,  made  into  a  paste  with 
water,  spread  on  the  two  sides  of  parallelopipedons  of  wood, 
dried  and  one  of  the  sides,  when   dry,  rubbed  over  with  lamp- 
black, the  following  result  was  obtained  : 

69 


MEMOIRS     ON 
TABLE  VII. 


RADIATION 

AT  212° 

NAME  OF  SUBSTANCE. 

WHITE  SIDE. 

BLACK  SIDE. 

Table  salt     

S3  1 

100 

White  su^ar  

98.7 

100 

Alum  

100.0 

100 

Sulphate  of  potash 

881 

100 

Nitrate  of  potash     .  . 

867 

100 

45.  Tims  we  see  that  table  salt  being  white  for   heat,  the 
radiation  of  the  white  side  is  less  than  that  of  the  black  side  ; 
and  further,  white  sugar  and  alum  being  both  nearly  black  for 
heat,  the  radiation  of  the  one  side  is  nearly  equal   to  that  of 
the  other.     We  see,  moreover,    that  sulphate   of   potash    and 
nitrate  of  potash,  especially  the  latter,  are  white  for  heat,  al- 
though not  quite  so  much  so  as  table  salt.     May  we  not  there- 
fore presume  that  these  substances  are  diathermanous  ?     There 
is,  moreover,  the  following  method   of  confirming   the   testi- 
mony  in   favor  of   the  diathermancy   of  these   substances   as 
derived  from  this  experiment. 

46.  Table  salt  being  white  for  heat,  part  of  the  reflected 
heat  will  be    composed   of   rays  which     have   been    reflected 
from  the  internal  surfaces  of  crystals.     Such  rays  have  there- 
fore been  sifted,  having  left  behind  that  description   of  heat 
which  passes  with  difficulty  through  rock  salt   and  also  (Art. 
9)  through  mica.     The  whole  reflected  heat  from  a  surface  of 
table  salt   should  therefore    be  of  a  nature  which  passes  more 
easily  through  mica   than   ordinary  heat,   and    (First    Series, 
Arts.  31  and  33)  since  the  sum  of  the  reflected  and  the  radi- 
ated heat  is  equal  both  in  quantity  and  quality  to    that  from 
lampblack,  it  follows   that  the  radiated  heat  from  table  salt 
(and  probably  from  other  substances  white  for  heat)  should,  in 
order  to  make  up  the  average  quality,  have  a  somewhat  greater 
difficulty  in  passing  through  mica    than  ordinary   lampblack 
heat.     Accordingly,  it  was  found  that   the   diathermancy  of  a 
mica  screen  for  heat  from  table  salt  was  less  than  that  for  or- 
dinary lampblack  heat  in  the    proportion  of  92  to  100,  while 
it  was  less  for  heat  from  pounded  sulphate  of  potash  in  the  pro- 
portion of  93  to  100,   thus   confirming   the  analogy   between 

70 


RADIATION  AND   ABSORPTION. 

rock  salt  and  sulphate  of  potash.     No  such  difference  was  ob- 
served for  heat  from  sugar. 

47.  We  see  also  from  the  above  table  that  the  radiation  and 
therefore   the  absorption  of   table  salt  is  83.1  per  cent,  leav- 
ing 16.9  per  cent  for  the  reflected  heat.     Now  Melloni  found 
that  chalk  absorbed  56.6  per  cent,  and  consequently  reflected 
43.4  percent,  of  heat  from  a  Locatelli  lamp;  and  if  we   sup- 
pose table  salt  to  be  at  least  as  white  as  chalk  for  heat  of  that 
temperature,  we  must  conclude  that  table  salt  is  less  white  for 
heat  of  212°,  than  for  heat  from  a  Locatelli  lamp,  following  in 
this  respect  the  same  law  as  chalk,   which,   from  being  nearly 
black  for  heat  at  212°,  becomes  comparatively  white  for  heat 
from  a  Locatelli  lamp.     There  is  also  little  doubt   that  table 
salt  reflects  more  than  16.9  per  cent  of  the  light  that  falls  upon 
it.     Hence  we  may  conclude  generally  that  powders   even  of 
diathermanous  bodies  are  less  white  for  heat  of  low  tempera- 
ture than  for  heat  of  high  temperature  and  for  light. 

48.  It   would   also   seem,    that,    although   comparing    one 
powder  with  another,  there  is  no   relation  between   apparent 
whiteness  and  whiteness  for  heat,  since  it  was  found  that  very 
white  surfaces  of  pounded  sugar  and  alum  (the  particles  com- 
pressed, not  made  into  a  paste  with  water)  reflected  little  or  no 
heat  ;  yet,  comparing  powdered  surfaces  of  the  same  diather- 
manous body  together,  there  seems  to  be  some  relation  between 
their  apparent   whiteness   and  their   whiteness   for   heat,    in- 
sufficient pounding,  or  any  circumstance  which  diminishes  the 
apparent  whiteness,  diminishing  also  its  whiteness  for  heat. 


71 


MEMOIRS  ON  RADIATION  AND  ABSORPTION. 

BIOGRAPHICAL  SKETCH. 

BALFOUR  STEWART  was  born  Nov.  1,  1828  at  Edinburgh. 
He  studied  at  the  Universities  of  St.  Andrews  and  Edinburgh, 
and  later  entered  upon  commercial  life.  His  particular  taste 
for  physical  science  soon  developed  itself,  however,  and  we  have 
in  1858  a  couple  of  his  earliest  papers.  He  became  associated 
with  Kelland  and  Forbes  at  this  time  and  in  1858  contributed 
his  most  important  work  on  the  extension  of  Prevost's  Theory 
of  Exchanges  in  radiation.  With  the  elaborate  (at  that  time) 
facilities  at  his  command  he  was  able  to  demonstrate  the  equal- 
ity of  the  radiating  and  absorbing  power  of  every  substance. 
For  this  and  other  work  he  was  awarded  the  Rom  ford  Medal 
some  years  later.  In  1859  he  was  appointed  director  of  the 
Kew  Observatory,  where  for  eleven  years  he  directed  the  im- 
portant studies  and  investigations  carried  on  there.  During 
this  period  he  was  seriously  injured  in  an  accident  from  which 
he  never  recovered.  In  1870  he  was  appointed  to  the  chair 
of  Physics  in  Owens  College,  Manchester,  which  he  occupied 
until  his  death  Dec.  19,  1887.  During  this  time  he  issued 
his  well-known  texts  in  Physics.  His  "  Conservation  of 
Energy,"  "  The  Unseen  Universe"  (in  conjunction  with  Tait), 
his  experiments  on  the  viscosity  of  ether,  etc.,  all  illustrate  the 
comprehensiveness  of  his  mind  and  the  originality  of  his 
genius. 


ON  THE  RELATION  BETWEEN  THE 

EMISSIVE  AND  THE  ABSORPTIVE 

POWER  OP  BODIES  FOR 

HEAT  AND  LIGHT. 


BY 

G.  R.  KIRCHHOFF. 


Reprinted  from  "  Investigations  on  the  Solar  Spectrum  and 
the  Spectra  of  the  Chemical  Elements,"  2d.  Edition,  Berlin, 
Ferd.  Dummler's  Publishing  House,  1866,  Gesammelte  Abhand- 
lungen,  pp.  571-598,  Leipzig,  1882. 


73 


A 

CONTENTS 


PAGE 

Nature  of  Heat  Rays  and  Light  Rays         .         .         .         .  75 

#/#6'&  Bodies  defined    .         .        .         .         .         .         .         .  76 

Definitions            .         .       -.         .         .         .       ..  .•       .         .  77 

Ratio  between  the  Emissive  and  the  Absorptive  Poiver  .  78 
Proof  of  the  Law  of  Emission  and  Absorption  for  Black 

Bodies .:  78 

Proof  of  the  Law  of  Emission  and  bAsorption  for  Any 

Body ,  .  89 

Generalization  of  the  Law  of  Emission  and  Absorption  .  92 

Some  Results  of  the  Law  ,  .  ' .  '  •  .  .  »  .  94 


ON  THE  RELATION  BETWEEN  THE 

EMISSIVE  AND  THE  ABSORPTIVE 

POWER  OP  BODIES  FOR 

HEAT  AND  LIGHT.' 

§1 

HEAT  rays  have  the  same  nature  as  light  rays  ;  these  con- 
stitute a  special  class  of  the  former.  The  invisible  heat  rays 
are  distinguished  from  light  rays  only  by  the  period  of  vibra- 
tion or  the  wave  length.  All  heat  rays  follow  the  same  laws 
in  their  propagation,  which  are  known  for  light  rays.  A 
luminous  body  in  space  sends  out  light  rays  that  are  indepen- 
dent of  the  bodies  on  which  they  fall  ;  similarly  all  heat  rays 
which  a  body  sends  out  are  independent  of  the  bodies  which 
form  its  environment. 

Of  the  heat  rays  that  are  sent  out  to  a  body  by  its  surround- 
ings a  part  are  absorbed,  the  others  are  sent  on  in  directions 
which  are  varied  by  reflection  and  refraction.  The  rays  re- 
fracted and  reflected  by  it  pass  off  along  with  those  sent  out  by 
it,  without  any  mutual  disturbance  taking  place. 

Through  the  radiations  which  a  body  sends  out,  the  quantity 
of  heat  which  it  contains  will,  according  to  the  law,  sustain  a 
loss  which  is  equivalent  to  the  vis  viva  of  those  rays  and, 
through  the  heat  rays  which  it  absorbs,  a  gain  which  is  equiv- 
alent to  the  vis  viva  of  the  absorbed  rays.  But  in  certain  cases 
an  exception  to  this  rule  may  occur,  in  that  the  absorption  and 
the  radiation  produce  other  changes  in  the  body,  as  for  ex- 
ample in  bodies  which  are  chemically  changed  by  light,  and 
light  absorbing  media  which  lose  their  power  of  shining 


1    Investigations  on  the  solar  spectrum  and  the  spectra  of  the  chem- 
ical elements,   2d.  Edition,    Berlin,   Ferd.  Dummler's  publishing  house 

1862. 

75 


MEMOIRS     ON 

through  the  radiation  of  the  light  which  they  have  absorbed. 
Such  cases  should  be  excluded  on  the  assumption  that  neither  by 
means  of  the  rays  which  it  radiates  or  absorbs,  nor  by  means  of 
other  influences  to  which  it  is  exposed,  does  the  body  possess  the 
power  to  undergo  a  change,  if  its  temperature  is  kept  constant  by 
the  addition  or  the  subtraction  of  heat.  Under  these  conditions, 
according  to  the  law  of  equivalence  of  heat  and  work,  the 
amount  of  heat  which  must  be  transferred  to  a  body  in  a  given 
time  to  prevent  cooling,  which  would  occur  in  consequence  of 
its  radiation,  is  equivalent  to  the  vis  viva  of  the  emitted  rays  ; 
and  the  amount  of  heat  which  must  be  withdrawn  in  order  to 
counterbalance  the  heating  from  absorption  of  radiations,  is 
equivalent  to  the  vis  viva  of  the  absorbed  rays. 

Let  a  body  which  satisfies  these  conditions  be  surrounded  by 
an  enclosure,  having  the  same  temperature,  through  which  no 
heat  rays  can  penetrate,  whose  temperature  is  kept  constant 
and  which  satisfies  the  same  conditions.  The  body  sends  out 
heat  rays  and  is  encountered  by  such  heat  rays,  which,  in  part, 
proceed  from  the  enclosure,  in  part,  are  thrown  back  to  the 
same  by  reflection  from  it,  absorbing  a  part  of  them.  Its  tem- 
perature must  thus  remain  the  same,  unless  heat  is  withdrawn 
from  it  or  communicated  to  it  as  follows  on  the  principle  from 
which  Carnot's  law  results.  For  this  reason,  the  vis  viva  of 
the  rays,  which  it  sends  out  in  a  certain  time,  must  equal  the 
vis  viva  of  the  rays  which  it  absorbs  in  the  same  time. 

The  proof  which  rests  upon  this  conclusion  requires  the  ac- 
curate investigation  of  the  rays  that  travel  back  and  forth  be- 
tween the  body  and  the  enclosure.  This  investigation  will  be 
much  simplified  if  we  imagine  the  enclosure  to  be  composed, 
wholly  or  in  great  part,  of  bodies  which,  for  infinitely  small 
thickness,  completely  absorb  all  rays  which  fall  upon  them. 

I  will  call  such  bodies  perfectly  black,  or  more  briefly  black. 
A  black  body,  in  this  sense  of  the  word,  must  have  the  same  re- 
fractive index  as  the  medium  in  which  the  radiation  takes 
place  ;  then  there  will  be  no  reflection  at  its  surface,  and  all  in- 
cident rays  will  be  wholly  absorbed.  Thick  iodine  vapour  in 
contact  with  air,  or  pitch  in  contact  with  glass,  may  be  treated 
as  black  bodies,  approximately,  but  not  iodine  vapour  in  con- 
tact with  glass  or  pitch  in  contact  with  air.  Next,  the  radia- 

76 


RADIATION   AND   ABSORPTION. 

tion  in  empty  space  will  be  investigated  ;  the  Mack  bodies  re- 
ferred to  must  therefore  have  a  refracted  index  which  differs 
only  infinitely  little  from  1. 

The  assumption  that  such  black  bodies  are  conceivable  forms 
an  important  aid  in  the  proof  which  will  be  presented  here. 
Further,  it  will  be  assumed  that  perfectly  diathermanous 
bodies  are  conceivable,  that  is,  such  which  will  absorb  none  of 
the  incident  heat  rays  of  whatever  nature  these  may  be,  and 
finally,  that  a  perfect  mirror  is  conceivable,  i.e.,  a  body  which 
reflects  completely  all  heat  rays.  A  perfect  mirror,  like  every 
diathermanous  body,  can  itself  send  out  no  rays  ;  for  if  it  did 
(confined  in  an  enclosure  of  like  temperature)  it  would  warm 
this  enclosure  more  and  more  and  cool  itself  more  and  more. 

o  n 

DEFINITIONS. 

Before  a  body  C,  Figure  1,  imagine  two  screens,  /Si  and  Sz  placed 
in  which  are  two  openings  1  and  2,  whose  dimensions  are  infi- 
nitely small  with  respect  to  their  distance 
apart,  and  each  of  which  has  a  center.      s* 

Through  these  openings  passes  a  pencil 
of  rays  sent  out  by  the  body  C.  Of  this 
pencil  of  rays,  let  us  consider  the  part, 
whose  wave  length  lies  between  A  and 
/i-j-rJA,  and  let  this  be  divided  into  two  n 

polarized  components,  whose  planes  of 
polarization  are  the  planes  a  and  b  per- 
pendicular to  each  other,  passing  through 
the  axis  of  the  ray  pencil. 

Let  E&\  be  the  intensity  of  the  com- 


ponent polarized  in  a,  or,  what  is  the  same  thing,  the  increase, 
which  the  vis  viva  of  the  ether  beyond  the  screen  S%  experiences 
through  this  component  in  the  unit  of  time.  The  quantity 
E  is  called  the  emissive  power  of  the  body  C. 

Conversely,  upon  the  body  C  there  falls  through  the  open- 
ings 2  and  1  a  pencil  of  rays  having  the  wave  length  A,  polar- 
ized in  the  plane  a;  of  this,  the  body  absorbs  a  part  while  it 
reflects  or  transmits  the  remainder  ;  let  the  ratio  of  the  inten- 


MEMOIRS     ON 

sity  of  the  absorbed  rays  to  the  incident  rays  be  A  and  let  this 
be  called  the  absorptive  power  of  the  body  C.  The  quantities 
^and  A  depend  upon  the  nature  of  the  condition  of  the  body 
6',  besides  also  upon  the  form  and  position  of  the  openings  1 
and  2,  the  wave  length  A  and  the  direction  of  the  plane  a. 

§3. 

Under  these  conditions  the  following  law  holds  :  The  ratio  be- 
tween the  emissive  and  the  absorptive  power  is  the  same  for  all 
bodies  at  the  same  temperature. 

This  law  will  be  proven,  first,  for  the  case  where  only  black 
bodies  are  compared  with  each  other,  that  is,  those  whose 
absorptic  power  =  1 ;  i.  e.,  it  will  be  shown  that  the  radiating 
power  of  all  black  bodies  is  the  same  at  the  same  temperature. 

The  proof  of  this  special  law  is  similar  to  that  of  the  general 
law,  but  simpler  ;  it  will  therefore  facilitate  the  understanding 
of  the  latter.  Moreover,  conclusions  which  are  drawn  from 
the  special  law  will  be  used  in  the  proof  of  the  common  law. 

§4. 

Proof  of  the  Law  §  3  for  Hack  bodies. 

Let  (7  be  a  black  body  ;  let  its  emissive  power,  which  is  com- 
monly indicated  by  E,  be  called  e ;  it  will  be  proven  that  e 
remains  unchanged,  when  C  is  replaced  by  any  other  black 
body  of  the  same  temperature. 

Imagine  the  body  C' enclosed  in  a  black  covering,  of  which 
the  screen  82  forms  a  part,  let  the  second  screen  182,  like  the 
first,  be  made  of  black  substance  and  let  both  be  united  with 
each  other  on  all  sides  by  black  walls,  as  shown  in  Figure  2. 
Suppose  the  opening  2  to  be  closed  at  first  by  a  black  surface, 
which  I  will  call  surface  2.  The  whole  system  must  have  the 
same  temperature  and  the  covering  be  maintained  at  a  constant 
temperature  throughout.  According  to  the  statements  made 
in  Figure  2,  §  1,  the  vis  viva  of  the  rays  which  the  body  C" sends 
out  in  the  given  time,  must  then  equal  the  vis  viva  of  the  rays, 
which  it  absorbs  in  the  same  time  ;  in  other  words  :  the  sum  of 
the  intensities  of  the  rays  which  it  sends  out  must  equal  the  sum 
of  the  intensities  of  the  rays  which  strike  it,  since  according  to 

78 


KADI AT ION    AND    ABSORPTION. 

supposition  it  completely  absorbs  the  latter.     Now  suppose  the 

surface  2  removed,  and  the  opening  closed  by  a  portion  of  a 

perfectly  reflecting  spherical  surface,  placed  directly  back  of  it 

and  having  its  center  at  the  middle  point  of  the  opening  1. 

Equilibrium  of  temperature  will  then  exist.     There  must  also 

be  equality  between  the  intensity  of  the  rays  which  the  body  C 

sends  out,  and  of  those  incident  upon  it.     Since  the  body  C 

now  sends  out  the  same  rays  as  in  the  cases 

previously  considered,    it  follows  that  the 

intensities  of  the  rays  incident  upon  C  are 

the  same  in  both  cases.     By  the  removal  of 

surface  2  the  rays  are  withdrawn  from  C 

which  pass  through  opening  1 ;  therefore 

the   concave   mirror   placed   at   opening  2 

throws  just  the  same  rays  back  to  C  which 

this  sends  out  itself  through  the  openings 

1  and  2,  for  the  concave  mirror  forms  from 

opening  1  an  image  which  coincides  with 

itself.1 


The  law  given  would  therefore  be  proved 

if  all  rays  of  the  two  pencils  compared  have  the  wave  length 
\  and  are  polarized  in  the  plane  a.  Both  pencils  of  rays, 
however,  are  made  up  of  different  components  and  form  the 
equality  of  the  intensity  of  the  whole  pencil.  "We  may  not 
directly  infer  the  equality  of  the  intensity  of  corresponding 
parts. 

The  necessary  completion  of  the  proof  may  easily  be  given 
when  a  plate  is  supposed  to  exist,  having  the  property  of  trans- 
mitting undiminished  rays  whose  wave  length  lies  between  a 
and  A  +  <tt.  and  whose  plane  of  polarization  is  parallel  to  the 
plane  a;  but  which  completely  reflects  rays  of  other  wave 


1  The  diffraction  of  the  rays  at  the  edges  of  opening  2  may  he  neg- 
lected, since  the  openings  1  and  2  may  be  assumed  infinitely  small  with 
respect  to  their  distance  and  yet  infinitely  great  with  respect  to  the 
wave  length,  that  is,  so  great,  that  the  defraction  may  be  inappreciable. 

From  this  it  follows  that  the  intensity  of  the  pencil  of  rays,  which  the 
body  C  sends  ont  through  openings  1  and  2,  equals  the  intensity  of  the 
pencil  of  rays  which  the  black  surface  2  sends  out  through  the  opening 
1.  Since  this  intensity  is  independent  of  the  form  and  further  character 
of  the  black  body  C,  so,  likewise,  is  the  former. 

79 


MEMOIRS     ON 


lengths  or  of  an  opposite  polarization.  If  we  should  imagine 
the  arrangement  shown  in  Figure  2  modified  by  bringing  such 
a  plate  before  opening  1,  then  we  may  immediately  arrive  at 
the  law  to  be  proved  by  the  treatment  employed  in  respect  to 
this  figure. 

The  assumption  that  such  a  plate  is  possible  is  in  no  wise 
justified.  On  the  contrary,  a  plate  is  possible  which,  of  the 
rays  striking  it  at  the  same  angle,  transmits  and  reflects  them 
in  different  degrees  according  to  their  wave  length  and  plane 
of  polarization.  A  plate,  which  is  so  thin  that  the  colors  of 
thin  films  are  visible  and  which  is  placed  obliquely  in  the  path, 
shows  this. 

Such  a  plate  is  required  for  the  investigation  under  consid- 
eration in  order  to  compare  them.  Besides  this,  it  is  necessary 
to  make  such  an  arrangement  that  both  pencils  of  rays  do  not 
pass  through  the  plate,  but  are  reflected  from  it  at  the  polariz- 
ing angle,  the  plane  of  reflection  coinciding  with  the  plane  a. 
This  is  advantageous  in  as  much  as  the  rays  polarized  perpen- 
dicularly to  a  need  not  be  considered.  Further,  the  plate  must 
be  made  of  a  perfectly  diathermanous  medium,  it  will  then 
absorb  no  rays  and  send  out  none. 

§£* 
0. 

In  the  arrangement  described  in  Figure  2  imagine  a  plate  of 
s2  the  kind  described  and  designated   as  P, 

brought  between  the  openings  1  and  2  (Fig. 
3).  Let  it  be  so  placed  that  the  pencil  of 
rays  passing  through  the  openings  1  and  2  is 
incident  at  the  polarizing  angle  and  the 
plane  of  incidence  is  the  plane  a.  Let  the 
wall  which  unites  the  screens  Si  and  83  be 
so  shaped  that  the  image,  which  the  plate 
P  casts  from  the  opening  2  lies  within  it  ; 
in  the  place  and  of  the  form  of  this  image 
imagine  an  opening  which  I  will  call  open- 
ing 3.  Let  opening  2  be  closed  by  a  black 
surface  of  the  temperature  of  the  whole 
system,  and  let  opening  3  be  closed  in  the  first  place  by  a 
similar  surface,  and  in  the  second  place  by  a  perfect  concave 

80 


RADIATION  AND  ABSORPTION. 

mirror  having  its  center  where  the  plate  P  forms  the  image  of 
the  middle  of  opening  1.  In  both  cases  the  equilibrium  of 
temperature  is  maintained ;  through  consideration  given  in 
the  preceding  paragraph,  it  follows  therefore  that  the  sum  of 
the  intensities  of  the  rays,  which  the  body  C  is  deprived  of 
through  the  removal  of  surface  3  equals  the  sum  of  the  inten- 
sities of  the  rays  which  are  brought  to  it  through  the  agency 
of  the  concave  mirror.  Let  a  black  screen  SB  (of  the  temper- 
ature of  the  whole  system)  be  so  placed  that  none  of  the 
rays  which  surface  3  sends  out  are  directly  incident  upon 
opening  1.  The  first  sum,  then,  is  the  intensity  of  the  rays 
which  proceed  from  surface  3,  and  are  reflected  by  plate  P  and 
pass  through  opening  1;  they  will  be  designated  by  Q.  The 
second  sum  is  made  up  of  two  parts  ;  one  component  comes 
from  C  and  is  : 

00 

d/.er2 

o 

where  r  represents  a  quantity  dependent  upon  the  nature  of 
the  plate  P  and  the  wave  length  A;  the  second  part  consists  of 
rays  which  have  come  from  a  portion  of  the  black  wall  which 
unites  the  screen  Sl  and  $2,have  passed  through  the  plate  P 
and  been  reflected  from  the  concave  mirror,  and  then  from  the 
plate  P;  this  part  will  be  designated  as  R.  It  is  unnecessary 
to  examine  further  the  value  of  R;  it  suffices  to  notice  that  R, 
as  well  as  Q,  is  independent  of  the  nature  of  C.  Between  the 
magnitudes  introduced  there  exists  the  equation  : 

:/eV2  -f-  R  =  Q 

If  we  now  imagine  the  body  C  replaced  by  another  black 
body  of  the  same  temperature,  letting  e  indicate  for  this  what 
e  has  represented  for  the  other,  there  exists  the  equation 

00 

<T/e'r2  -f  E  =  Q 
o 

From  this  it  follows  that 

dl.  (e—e')  r'2=  0 

Let  us  now  assume  that  the  index  of  refraction  of  the  plate  P 

81 


MEMOIRS     ON 

differs  but  little  from  unity.  From  the  theory  of  the  colors  of 
thin  plates  it  follows  then  that  we  can  place 

r  =  p  sin2  -?- 

A 

where  p  represents  a  quantity  proportional  to  the  thickness  of 
the  plate  P,  independent  of  A,  and  a  quantity  independent  of 
this  thickness.  From  this  follows  the  deduced  equation  : 


o 

'  Since  this  equation  must  hold  for  every  thickness  of  the 
plate  P>  and  hence  for  every  value  of  p,  it  follows  that  for 
every  value  A  we  may  conclude  that 


To  prove  this,  substitute  in  that  equation  for  sin*  ~- : 

A 

i(cos4  ~ — 4  cos  2  ~  _i_Q) 

A  A      '        ' 

and  differentiate  twice  with  respect  to  p :  we  then  have 

4  -f-  —  cos  2  f-  )  =  0 

In  place  of  A  let  us  introduce  a  new  quantity  into  the  equa- 
tion ;  where 


-?-=a 

A 


and  set 

we  thus  obtain 


00 

daf  (a)  (cos  2  p  a  —  cos  p  a)  =0 


If  we  consider  that  when  0  (a)  represents  any  arbitrary  func- 
tion of  a 

J°°  /*°°  a 

da?  (a)  cos  2 pa  =  £    I     da<j>  (  -~- )  cos  pa 
o  *J  o 

from  which  we  may  conclude  that  if  we  substitute  —for  c,  we 
may  therefore  write 

00  a 

d*  \f(  — g-  )  —  2/  (a)]  cos  p  a  =  0 
o 

82 


RADIATION   AND   ABSORPTION. 

Multiply  this  equation  by  dp  cos  xp,  where  x  represents  an  arbi- 
trary quantity,  and  integrate  it  from  p  =  0  to  p  =  oo.  Accord- 
ing to  Fourier's  formula  which  is  expressed  by  the  equation 

/*°°  C**  TT 

I      dpcospx    I       da^  (a)  cos  pa  =   —  $  (x) 
Jo  Jo  2 

we  have 

OP  /(-I.  )  =  2/(a) 


From  this  it  follows  that  /(a)  either  vanishes  for  all  values 
of  a,  or  becomes  infinitely  great  when  a  approaches  zero.  When 
a  approaches  zero  A  becomes  infinite.  If  we  remember  the 
meaning  of  /(a)  and  consider  that  p  is  a  proper  fraction,  and 
that  neither  e  nor  e'  can  become  infinite  when  A  increases  to 
infinity,  then  it  is  evident  that  the  second  case  cannot  exist 
and  therefore,  that  for  all  values  of  A,  e  =  e'. 

In  a  similar  way  we  may  treat  the  case  when  C  is  not  a  black 
body  but  is  an  arbitrary  one.  We  shall  not  assume  for  the 
same  that  it  is  homogeneous  ;  partly  on  its  surface,  partly  in  its 
interior  will  the  rays  therefore,  which  are  incident  upon  it  from 
the  black  envelope,  experience  the  most  manifold  modifications. 
On  these  grounds,  there  must  be,  as  a  preliminary  to  the  pro- 
posed proof,  a  study  made  of  the  radiation  which  takes  place 
between  black  surfaces  of  the  same  temperature,  for  arbitrary 
bodies.  To  this  investigation,  which  depends  upon  the  formula 
just  proved,  the  following  paragraphs  are  devoted. 

§6. 

MUTUAL  RADIATIONS  OF  BLACK  SURFACES. 
If  the  pencil  of  rays  which  the  body  C  sends  out  through 
openings  1  and  2  should  be  partly  linearly  polarized,  the  plane 
of  polarization  of  the  polarized  portion  must  rotate  when  C  is 
rotated  around  the  axis  of  the  pencil.  Such  a  rotation  must 
therefore  change  the  value  of  e.  Since,  according  to  the  equa- 
tion proved,  such  a  change  cannot  take  place,  the  pencil  of 
rays  can  have  no  linearly  polarized  portion.  It  can  be  proved 
also,  that  it  can  have  no  circularly  polarized  part.  But  the 
proof  for  this  will  not  be  given  here. 

We  will  also  grant,  without  this,  that  black  bodies  are  con- 

83 


MEMOIKS  ON 

ceivable  in  whose  structure  there  is  no  reason  why  they  should 
send  out  in  any  direction  more  right  handed  circularly  polarized 
rays  than  left  handed  circularly  polarized  rays. 

Of  this  character  will  the  black  bodies,  concerned  in  the  fur- 
ther treatment,  be  assumed ;  they  send  out  in  all  directions 
unpolarized  rays. 

o    ty 

The  quantity  represented  by  e  depends,  aside  from  the  tem- 
perature and  wave  length,  on  the  form  and  the  relative  position 
of  the  openings  1  and  2.  If  w\,  w?  represent  the  projections  of 
the  openings  upon  planes  perpendicular  to  the  axis  of  the  pen- 
cil, and  if  s  is  called  the  distance  of  the  openings,  then 


where  /is  a  function  of  the  wave  length  of  the  temperature 
only. 

§8. 

Since  the  form  of  a  body  C  is  arbitrary,  a  surface  may  be 
substituted,  which  exactly  fills  opening  1  and  which  I  will  call 
surface  1  ;  the  screen  Si  may  then  be  imagined  removed.  Fur- 
ther the  screen  $2  may  be  considered  removed  if  the  pencils  of 
rays  which  e  covers,  is  defined  as  that  which  falls  from  surface 
1  upon  surface  2,  which  the  opening  2  exactly  fills. 

§  9. 

A  consequence  of  the  last  equation,  which  immediately  fol- 
lows and  which  will  later  be  used,  is  that  the  value  e  remains 
unchanged  if  we  imagine  the  openings  1  and  2  interchanged. 


We  will  now  establish  a  law  which  may  be  treated  as  a  gen- 
eralization of  the  law  presented  in  the  last  paragraph. 

Between  the  two  black  surfaces  of  the  same  temperature  1 
and  2,  is  placed  a  body  which  may  refract,  reflect,  or  absorb  in 
any  way  the  rays  which  one  sends  to  the  other.  Several  pencils 
of  rays  may  pass  from  surface  1  to  surface  2  ;  choose  one  of 
these,  and  consider  the  part  of  the  one  at  1  whose  wave  length 
lies  between  A  and  A  -f  eZ/i,  and  divide  this  into  two  components 

84 


RADIATION   AND    ABSORPTION, 

whose  planes  of  polarization  are  the  planes  of  a\  and  b\  which 
are  perpendicular  to  each  other  (otherwise  arbitrary).  Let  the 
part  of  the  first  component  which  enters  2  be  divided  into  two 
components  whose  planes  of  polarization  are  the  planes  a2  and 
b2  perpendicular  to  each  other  (otherwise  arbitrary).  Let  the 
intensity  of  the  component  polarized  in  «2  be  Kd'k.  Of  the 
pencil  of  rays  which  passes  over  the  same  path  as  the  preceding 
one,  from  2  to  1,  let  us  consider  the  part  at  2  whose  wave 
length  lies  between  A  and  a  +  dA,  and  divide  this  into  two  com- 
ponents polarized  in  #2  and  Z>2.  Divide  the  portion,  which 
reaches  1  from  the  first  component,  into  two  parts  whose  planes 
of  polarization  are  a\  and  b\.  Let  the  intensity  of  the  com- 
ponents polarized  in  a\  be  K'd'\.  Then 

The  proof  of  this  law  will  be  made  upon  the  assumption  that 
the  rays  under  consideration  undergo  no  weakening  in  their 
path,  and  also  upon  the  assumption  that  refraction  and  reflec- 
tion occur  without  loss,  that  there  is  no  absorption  and  that 
the  rays,  coming  from  1,  polarized  in  a\,  reach  2  polarized  in  «2, 
and  vice  versa. 

Through  the  middle  point  of  1  pass  a  plane  perpendicular  to 
the  axis  of  the  pencil  of  rays,  either  incident  or  emergent  at 
this  point,  and  imagine  in  this  a  right-angled  coordinate  sys- 
tem, whose  origin  is  that  middle  point.  Let 
x\  y\  be  coordinates  of  any  point  in  the  plane, 
Figure  4.  At  the  distance  of  unity  from  this 
plane,  imagine  a  second,  parallel  to  it,  and  iu 
this,  a  coordinate  system  whose  axes  are  parallel 
to  each  of  those,  and  whose  origin  lies  in  the 
axis  of  the  pencil  of  rays.  Let  Xs  y$  be  coordi- 


nates of  any  point  in  this  plane.     In  a  similar 
FIG.  4.  manner  pass  through  the  middle  point  of  2,  a 

plane  perpendicular  to  the  axis  of  the  bundle  of  rays,  incident 
or  emergent  at  this  point,  and  introduce  in  this,  a  rectangular 
system  of  coordinates  whose  origin  is  the  middle  point  men- 
tioned. Let  x2  y<2  be  coordinates  of  a  point  in  this  plane. 
Finally,  at  a  distance  of  unity  from  this  plane  and  parallel  to 
it  imagine  a  fourth,  and  in  it  a  system  of  coordinates  whose 
axes  are  parallel  to  the  axis  of  x*,  y?  and  whose  origin  lies  in 

85 


MEMOIRS     ON 

the  axis  of  the  pencil  of  rays.     Let  x±,  y±  be  coordinates  of  any 
point  in  this  fourth  plane. 

From  an  arbitrary  point  let  a  ray  pass  to  any  other  point 
(#2,  #2)  ;  let  Tb&  the  time  required  to  pass  from  one  point  to 
the  other ;  we  will  suppose  it  to  be  a  known  function  of  x\,  y\, 
#2,  y<2>  If  the  points  (x3,  y3)  and  (x±,  y*)  He  in  the  path  of  the 
ray  referred  to,  (and  if  for  the  sake  of  brevity  the  velocity  of 
the  ray  in  vacua  be  taken  as  unity)  the  time  which  the  ray  re- 
quires to  pass  from  (x3,  y3)  to  (z4,  y*)  will  be 


-V 


Assuming  the  points  (#3,  2/3),  (#4,  y4)  given,  and  the  points 
(a?i,  y\),  (#2  #2)  required,  we  could  find  these  from  the  condition 
that  the  above  expression  is  a  minimum.  If  we  assume  that 
the  eight  coordinates  x\,  y\,  x2,  y2,  x3,  yz,  x±,  y±  are  infinitely 
small,  the  following  equations  express  the  condition  that  the 
four  points  (x\,  #1),  (z2,  2/2),  (#3,  #3),  (x±,  ?/4)  lie  in  one  ray  : 


dxl  '  dx2 

dT  dT 

Now  let  (xi,yi)  be  a  point  in  the  projection  of  surface  1  on  the 
plane  Xi,  y\  and  let  dx\9  dy\  be  an  element  of  this  projection  in 
Ayjiich  the  point  Xi,  y\  lies  and  which  is  infinitely  small  with 
respect  to  the  surfaces  1  and  2.  Let  (x3,  y3)  be  a  point  in  a 
ray  proceeding  from  (x\,  y\)  to  surface  2,  dx3,  dijs,  a  surface 
element  in  which  the  point  (x3,  y3)  lies,  of  the  same  order  as 
dx\,  dy\.  The  intensity  of  the  rays  of  the  required  wave 
length  and  of  the  given  plane  of  polarization,  which,  proceed- 
ing from  dx\,  dy\,  pass  through  dx3,  dy3,  is  then  according 
to§7; 

d\   I  dx\  dy\  dx3  dy3. 

According  to  the  supposition,  this  amount  of  rays  reaches 
surface  2  undiminished  and  forms  an  element  of  u  quantity  des- 
ignated by  Kdh.  JTis  the  definite  integral 

86 


RADIATION  AND  ABSOKPTiON. 


/   f  f  f  f 

\s     \s     \s     */ 


The  integration  here  with  respect  to  x%,  ?/3  is  to  be  taken 
over  those  values  which  these  quantities  have  according  to  the 
above  equations,  while  x\  and  y\  remain  constant  and  x2,i/2  have 
all  the  values  which  correspond  to  the  projections  of  surface  2 
upon  the  plane  #2,  y2.  The  integration  with  respect  to  x\,  y\ 
is  then  to  be  taken  over  the  projection  of  surface  1.  The 
double  integral 


dx3  dys  so  limited, 

«y    «y 

is,  however, 

/*  /*  / 

or  from  the  equations  for  z3,  f/3 

C  r  /    ^'2y      t)2r  ^2r    _— __ 

«/    »/    \^Xj  fix 2  by  i  by 2          '^     '*'"    'x/¥>    /*/"      *  ^^' 


where  the  integration  is  taken  over  the  projections  of  surface  2 
Whence 

C  C  C/    tfT       fPT  ^T        tfT     \ 

)dxidyi  dx2  dy% 


where  the  integration  is  taken  over  the  projections  of  surfaces 
1  and  2. 

If  the  magnitude  of  a  K'  be  treated  in  the  same  way,  remem- 
bering that  a  ray  requires  the  same  time  to  pass  over  a  path  be- 
tween two  points  in  either  direction,  the  same  expression 
will  be  found  for  K'  as  for  K.  Thus,  the  enunciated  law  is 
proved,  subject  to  the  limiting  conditions  under  which  it  will 
next  be  proved.  This  limitation  may,  however,  be  immediately 
disposed  of  by  an  observation  made  by  Helmholtz  in  his 
"Physiological  Optics,"  p.  169.  Helmholtz  says  here  (with 
somewhat  different  notation)  :  "  A  light  ray  passes  from  point 
1  to  point  2  after  any  number  of  refractions,  reflections,  etc. 
Through  1  suppose  two  arbitrary  planes  a\  and  #1  passed  in  the 
direction  of  the  ray  perpendicular  to  each  other,  in  which  its 
vibrations  are  supposed  to  be  resolved.  Two  similar  planes,  «2 
and  #2  are  also  passed  through  the  ray  at  2.  Then  the  following 

87 


MEMOIRS     ON 

may  be  proved  :  If  a  quantity  i  of  light  polarized  in  the 
plane  a\  proceeds  from  1  in  the  direction  of  the  ray  mentioned 
and  of  this,  the  quantity  k  of  light  polarized  in  the  plane  a\ 
reaches  2,  so  will  vice  versa  the  quantity  k  of  light  polarized  in 
#2  reach  point  1  if  the  quantity  i  of  light  polarized  in  a2 
proceed  from  point  2."  1 

Applying  this  law,  and  representing   by  7   the  value   of  the 

ratio  4  for  the  two  rays  which  pass  in  either  direction  between 


the  points  (x\,  y\)  and  (#2,  3/2),  then  an  expression  is  obtained  for 
K  &s  well  as  for  K  which  differs  from  that  formed  only  in  that 
now  y  appears  as  a  factor  under  the  integral  sign. 

The  equality  of  ./Tand  7T'  exists  accordingly  when  >  has  a 
different  value  for  the  rays  into  which  one  of  the  pencils  com- 
pared may  be  divided  ;  for  example,  it  is  unaffected  if  a  part  of 
the  pencil  is  intercepted  by  a  screen. 


Of  the  same  pencils  which  were  compared  in  the  preceding 
paragraphs,  the  following  law  also  holds  :  of  the  pencil  passing 
from  1  to  2,  consider  the  part  at  2  whose  wave  lengths  lie  be- 
tween A  and  A  +  dl  and  resolve  this  into  two  components  polar- 
ized in  «2  and  #2  ;  let  the  intensity  of  the  first  component  be 
Hd'k.  Of  the  pencil  which  passes  from  2  to  1,  consider  at  2  the 
portion  whose  wave  lengths  lie  between  A  and  A  +  d%9  and  resolved 
this  into  two  components  polarized  in  a2  and  Z»2.  Let  the  por- 
tion of  the  first  component  reaching  point  1  be  H'd\. 

Then  H=ff'.  The  proof  of  this  law  is  the  following  ; 
^and  K  are  to  have  the  same  meaning  as  in  the  preceding 
paragraph  ;  let  L  and  L'  be  the  quantities  which  arise  form  K 
and  K'.  when  plane  a\  is  interchanged  with  plane  bi. 

1  The  law  of  Helraholtz,  as  he  himself  noted,  does  not  hold  good 
when  the  plane  of  polarization  of  a  ray  undergoes  any  rotation,  such  as 
magnetic  force  produces  according  to  Faraday's  discovery  ;  therefore, 
in  the  following  considerations  magnetic  force  must  not  be  considered 
as  present.  Helmholtz  limited  his  law  also  by  supposition  that  light 
undergoes  no  change  of  refrangibility  such  as  occurs  in  fluorescence  ; 
this  limitation  is  unnecessary  in  the  application  of  the  law,  if  rays  of 
only  a  given  wave  length  are  regarded. 

88 


RADIATION   AND   ABSORPTION. 

Then  L  =  L'}  similarly  K  =  K',  further  H—  K+  L,  because 
rays  polarized  perpendicularly  to  each  other  do  not  interfere, 
when  they  are  brought  back  to  a  common  plane  of  polarization 
in  case  they  are  a  part  of  an  unpolarized  ray  ;  and  according  to 
§  6  the  surface  1  sends  out  unpolarized  rays. 

Finally  H'  =  K+  L',  because  two  rays,  whose  planes  of  polar- 
ization are  perpendicular  to  each  other,  do  not  interfere. 
From  these  equations  it  follows  that  H=  H'. 


Let  Fig.  2  have  the  same  meaning  as  in  §  4,  only  let  the  body 
C  be  not  a  black  body  but  an  arbitrary  one.  Let  opening  2  be 
closed  by  surface  2.  This  surface  sends  out  a  pencil  of  rays 
through  opening  1  to  the  body  C,  which  is  partly  absorbed  by 
this  body,  and  partly  scattered  in  different  directions  by  reflec- 
tion and  refraction.  Of  this  pencil  consider  the  part  between 
1  and  2  whose  wave  lengths  lie  between  A  and  A  +  d\  and  resolve 
this  into  two  components  polarized  in  plane  a  and  the  plane 
perpendicular  to  this.  Let  that  part  of  the  first  component 
which  escapes  absorption  by  C,  and  hence  strikes  the  black  cov- 
ering in  which  the  body  C  is  inclosed,  be  M'd"k.  A  certain  por- 
tion of  the  rays  which  a  part  of  the  covering  sends  out  to  the 
body  C,  fall  upon  surface  2  through  opening  1  ;  thus  by  means 
of  the  body  C  a  pencil  of  rays  is  produced  which  passes  through 
opening  1  to  the  surface  2.  Of  this,  consider  the  part  whose 
wave  lengths  lie  between  A  and  A  +  dh  and  divide  it  into  two 
components  polarized  in  plane  a  and  the  plane  perpendicular 
to  it.  Let  the  intensity  of  the  first  components  be  Md\. 

Then  M=  M  '.  The  truth  of  this  law  follows  from  the  propo- 
sition from  the  preceding  paragraph,  if  we  apply  this  to  all 
pencils  of  rays,  which  surface  2  and  all  the  elements  of  the 
black  cover  surrounding  the  body  C  interchange  with  each 
other  by  means  of  the  body  C,  and  then  form  the  sum  of  the 
equations  so  obtained. 

§13. 

Proof  of  the  proposition  §#  for  any  body. 
Let  the  arrangement  shown  in  Fig.  3  and  described  in  §  5  be 


MEM OIKS     ON 

taken,  only  let  the  body  C  no  longer  be  a  black  body,  but  ar- 
bitrary. Ill  both  cases  described  there,  the  equilibrium  of  heat 
subsists  ;  then  the  vis  viva  which  is  drawn  out  from  the  body 
G  by  the  removal  of  the  black  surface  3,  must  therefore  be 
equal  to  the  vis  viva  which  is  supplied  to  this  by  the  presence 
of  the  concave  mirror.  The  symbols  used  in  §  5  will  be  used 
here  with  the  same  meaning.  The  letters  E  and  A  will  have 
the  meaning  given  them  in  §  2. 

If  surface  3  is  removed,  then  the  rays  are  withdrawn  from 
the  body  C  which  this  surface  sends  to  it ;  the  intensity  of  the 

x»  00 

part  of  these  rays  which  it  absorbed  is  =  f     cUer  A. 

*/  o 

Now  the  rays  must  be  examined  which  are  transmitted  to 
the  body  by  the  presence  of  the  concave  mirror.  All  these  rays 
must  be  reflected  from  the  concave  mirror  to  plate  P  and  from 
this  to  opening  1,  and  these  must  pass  in  the  same  direction  as 
if  they  came  from  opening  2.  Before  they  strike  the  concave 
mirror,  they  have  either  experienced  a  reflection  from  it  or  not. 
In  the  first  case  they  can  only  be  sent  back  again  to  the  con- 
cave mirror  by  means  of  the  body  (7  over  the  path  which  is  the 
reverse  of  that  already  described.  It  must  next  be  premised  that 
the  body  (7  has  such  a  position  that,  of  the  rays  which  pass  to 
it  through  2  and  1,  only  an  infinitely  small  part  will  be  re- 
flected back  again  through  opening  1  to  opening  2.  Then,  of  the 
rays  in  question,  only  an  infinitely  small  fraction  have  suffered 
multiple  reflection  at  the  concave  mirror,  audit  is  sufficient  to 
consider  those  which  are  reflected  only  once  at  the  mirror.  Of 
these,  a  part  proceed  from  the  body  (7,  the  rest  from  the  black 
covering.  The  first  part  has  experienced  a  double  reflection  at 
plate  P  ;  the  vis  viva  which  the  body  0  absorbs  from  it  is 

A. 

The  second  part  which  proceeds  from  the  black  enclosure 
may  again  be  considered  as  consisting  of  two  parts  ;  one  which 
passes  to  the  concave  mirror  without  the  mediation  of  the  body 
C.,  and  a  second,  by  means  of  it.  Each  arises  from  rays  which 
proceed  from  black  partition  opposite  the  concave  mirror, 
and  have  passed  through  the.  plate  P,  have  been  reflected  from 
the  concave  mirror  to  the  plate  P  and  from  this  to  opening  1. 

90 


RADIATION    AND    ABSORPTION. 

Without  examining  from  which  part  of  the  black  wall  these 
rays  have  proceeded,  their  intensity  may  be  found  by  the  law 
established  in  §  11. 

By  the  application  of  this,  the  intensity  of  those  rays  which 
were  absorbed  by  the  body  C  is  shown  to  be 

.00 

(/ACT  (1— r)A. 


Finally  in  order  to  find  the  intensity  of  the  rays  which  proceed 
from  the  black  covering  by  means  of  the  body  C  to  the  concave 
mirror,  and  pass  back  from  this  to  the  body  C  and  are  here 
absorbed,  let  N  designate  the  quantity  which  the  quantity  in- 
dicated by  M  in  §  12  becomes  in  consequence  of  plate  P  being 
brought  into  its  place  and  the  surface  3  removed  ;  the  intensity 

is  then  =   f    MNr*  A. 

J    o 

The  difference  between  M  and  N  arises  only  from  .the  varia- 
tion which  the  rays,  falling  upon  the  body  C  from  the  black 
covering  through  opening  1,  undergo  by  the  introduction  of 
plate  P  and  the  removal  of  surface  3.  Suppose  the  plate  P 
brought  into  its  position,  without  removing  surface  3,  then  M 
can  undergo  no  change,  since  all  the  pencils  of  rays,  which  go 
to  the  opening  1  remain  unchanged  ;  the  pencil  proceeding 
from  surface  2,  for  example,  suffers  a  loss  through  reflection  at 
plate  P  which  will  be  exactly  replaced  by  the  reflection  of  the 
rays  going  out  from  the  surface  3.  The  difference  M—N  is 
therefore  only  produced  by  the  removal  of  surface  3  and  is  also 
equal  to  the  part  of  M  which  arises  from  the  rays  sent  out  by 
surface  3  to  opening  1  by  means  of  plate  P.  According  to  the 
supposition  made  in  these  paragraphs  concerning  the  position 
of  the  body  C,  M—Nis  infinitely  small  in  comparison  with  the 
intensity  of  the  rays  of  equal  wave  length  which  surface  3 
sends  to  opening  1  by  means  of  plate  P,  as  well  as  infinitely 
small  in  comparison  with  the  intensity  of  rays  of  equal  wave 
length  and  polarized  in  the  plane  a,  which  surface  2  sends  to 
opening  1  by  the  absence  of  the  plate  P,  and  therefore  finite 
and  also  infinitely  small  with  respect  to  the  quantity  repre- 
sented by  M '  in  §  12  (assuming  that  1 — A  is  not  infinitely 
small).  Since,  however,  as  already  pointed  in  the  places  cited, 
M'  =  M ,  we  may  also  place 

91 


MEMOIRS     ON 

N*-M-~M', 

But  according  to  the  definition  given  of  M' 
M'  =  e  (1 — A)  and  therefore 

JOO  x,GO 

dA  Nf2  A  =    I       eZ/e  ( 1—^ )  r2  A. 
o  «y  o 

The  proposition  presented  at  the  beginning  of  this  paragraph 
would  then  be  expressed  by  the  equation  : 

JOO  x»00  s»CO  x»00 

o  */   o  */   o  */   o 

or  by  the  equation  f    ^  (E—Ae)  Af2  =  0. 

•J  o 

By  the  same  treatment  employed  in  §  5   with  reference  to  a 
similar   equation,    we  may  conclude  that   for  every  value  of  A* 

-  =e 
or  substituting  for  e  its  value  in  §  7. 

E_  _    j    Wi   W% 
A   =  82      * 

Thus,  the  law  §  3  is  proved  under  the  assumption  that,  of  the 
pencil  which  falls  from  surface  2  through  the  opening  1  upon 
the  body  (7,  no  finite  part  is  reflected  by  this  back  to  the 
surface^  ;  further,  that  the  law  holds  without  this  limitation, 
if  we  consider  that  when  the  condition  is  not  fulfilled,  it  is 
only  necessary  to  turn  the  body  C  infinitely  little  in  order  to 
satisfy  it,  and  that  by  such  a  rotation  the  quantities  ^and  A 
undergo  only  and  infinitely  small  change. 


A  Generalization  of  tlie  Laiv  §  3. 

The  discussions  given  assume  that  the  space  in  which  the 
radiation  occurs  is  a  vacuum.  But  the  same  treatment  also 
obtains  when  this  space  is  filled  with  any  perfectly  diather- 
manous  medium  ;  only  the  function  /  will  then  be  different 
than  in  the  former  case.  The  symbol  /may  then  be  retained 
for  a  vacuum  and  /'  may  be  called  the  corresponding  function 
of  temperature  and  wave  length  for  a  certain  diathermanous 
medium  ;  if  n  is  the  index  of  refraction  of  the  same  for  the 

92 


RADIATION   AND   ABSORPTION. 

temperature  and  wave  length  to  which  /  and  /'  refer,  then  a 
simple  relation  exists  between  I',  I,  and  n ;  the  same  follows 
from  the  law  already  demonstrated  as  will  be  here  shown. 

Imagine  a  layer  of  a  diathermanous  medium  bounded  by  two 
parallel  planes,  and  with  one  side  in  contact  with  the  black  sur- 
face F.     Let  the  thickness  of  the  layer=  1.     For  this  body,  the 
s ,  absorptive  power  of  A  ,  and  the  emis- 
sive power  E,  in  relation  to  a  certain 
pencil   of   rays   will   be    investigated. 
The  opening  1  and  2  which  determine 
the  form    of   the   pencil   will    be    in 
screens  S\  and  $2,  of  which  the  first 
covers  the  surface  of  the  layer  hither- 
tofore  supposed  to  be  free,  and  the  sec- 
ond   is   parallel   to    it;   let    the  line 
FIG.  5.  joining  the  middle  points  of  the  open- 

ings be  perpendicular  to  the  screens.  Of  any  pencil  of  rays 
of  a  definite  wave  length  and  direction  of  polarization,  which 
passes  from  the  opening  2  to  the  opening  1,  a  fraction  will  be 
reflected  at  the  latter  which  may  be  designated  by  p  ;  the  rest 
passes  to  the  surface  J^and  is  here  completely  absorbed  ;  there- 
fore 

To  find  E,  represent  by  x,  y  ;  x\,  y\  ;  and  #2,  y<*  the  coordi- 
nates of  a  point  of  the  surface  F,  the  opening  1,  and  the  open- 
ing 2,  reckoned  from  those  points  which  are  found  in  the  axis 
of  the  pencil.  If  these  points  lie  in  a  ray,  then  if  s  again  rep- 
resents the  distance  of  the  two  openings, 


must  be  a  minimum  with  respect  to  x\  and  y\  :  i.  e., 

x=Xl-x^-xi    y  =  yi—y*-yi 

ns       >  ns 

if  w\  and  w2  are  the  surfaces  of  the  two  openings,  we  find  by  a 
treatment,  which  is  given  in  a  more  general  form  in  §  10,  the 
intensity  of  the  rays  (polarized  in  a  and  of  wave  lengths  be- 
tween A  and  7i  +  d%)  which,  falling  from  J^upon  opening  1,  in 
part,  pass  to  opening  2, 

93 


MEMOIRS    ON 

by         dx 


,v     ,    . 

that  is 


Of  these  rays  the  fraction  1  —  p  goes  through  the  opening  1 
and  arrives  at  the  opening  2. 

Tims  E-  (1-,)  T-2tf*- 

If  these  values  of  E  and  A   are  substituted   in   the   equation 

E       I 
A  = 
then  r  = 


Results  of  the  Law  §  5. 
When  any  given  body  —  a  platinum  wire  for  instance  —  is 
gradually  heated,  it  emits,  up  to  a  certain  temperature,  only 
rays  whose  wave  lengths  are  greater  than  that  of  the  visible 
rays.  At  a  certain  temperature,  rays  of  the  wave  length  of  the 
extreme  red  begin  to  be  visible  ;  as  the  temperature  rises 
higher  and  higher,  rays  of  a  shorter  and  shorter  wave  length 
are  added,  so  that  for  every  temperature,  rays  of  a  corresponding 
wave  length  come  into  existence,  while  the  intensity  of  the 
rays  of  greater  wave  lengths  increase.  If  the  law  proven  be 
applied  to  this  case,  it  will  be  seen  that  the  function  /  for 
any  wave  length  vanishes  for  all  temperature  below  that  of  a 
certain  temperature,  depending  on  the  wave  length  for  higher 
temperatures  increases  with  the  same.  From  this  it  follows, 
when  the  same  law  is  applied  to  other  bodies,  that  all  bodies, 
whose  temperature  is  gradually  raised,  begin  to  send  out  rays 
of  the  same  wave  length  at  the  same  temperature,  and  begin  to 
glow  with  red  rays  at  the  same  temperature,  and  at  a  higher 
common  temperature,  yellow,  and  so  on.  The  intensity  of 
rays  of  a  certain  wave  length  which  different  bodies  send  out  at 
the  same  temperatures  may,  however,  be  very  different  ;  it  is 
proportional  to  the  absorptive  powers  of  bodies  for  rays  of  that 
particular  wave  length.  At  the  same  temperature  accordingly 
metal  glows  more  brightly  than  glass,  and  this  more  brightly 
than  a  gas.  A  body  that  remains  perfectly  transparent  at  the 

94 


RADIATION    AND    ABSORPTION. 

highest  temperature  would  never  become  incandescent.  Into 
a  ring  of  platinum  wire  of  about  5mm  diameter,  I  introduced 
some  phosphate  of  soda  and  heated  it  in  the  nonluminous  flame 
of  the  Bunsen  burner.  The  salt  melted  and  formed  a  fluid 
lens  and  remained  perfectly  clear;  but  it  emitted  no  light, 
while  the  platinum  ring  in  contact  with  it  radiated  the  most 
brilliant  light. 

Draper1  has  drawn  the  conclusion  from  investigations  that 
all  solid  bodies  begin  to  glow  at  the  same  temperature.  From 
his  researches  he  lias,  however,  noted  that  certain  bodies  like 
chalk,  marble,  fluor  spar  glow  at  a  lower  temperature  than 
they  should  according  to  this  law;  he  called  this  luminosity 
phosphorescence,  and  said  it  clearly  differed  from  glowing,  by 
the  color.  But  whatever  name  may  be  given  to  this  luminos- 
ity, it  is  in  contradiction  with  law,  §  3,  and  a  body  which  shows 
it  must  therefore  not  satisfy  the  assumptions  which  were  made 
in  the  proof  of  the  law,  that,  at  a  constant  temperature,  it  must 
remain  unchanged  ;  phosphorescence  is  not  purely  an  effect  of 
heat,  and  is  not  exclusively  determined  by  the  temperature, 
but  is  produced  by  changes  in  the  body  ;  if  these  changes — 
whether  they  are  chemical  or  of  another  nature — have  ceased 
then  the  phosphorescence  must  vanish. 

§16. 

From  the  law,  §  3,  it  follows  that  a  body,  which  absorbs  more 
rays  from  one  plane  of  polarization  than  from  another,  sends 
out  in  the  same  ratio  more  rays  from  the  first  plane  of  polar- 
ization than  from  the  second.  Consequently,  as  is  known  to 
happen,  a  glowing  opaque  body  having  a  smooth  surface  sends 
out  light  in  directions  oblique  to  this  surface  which  is 
partially  polarized  perpendicularly  to  the  plane  passing 
through  the  ray  and  the  normal  to  the  surface  ;  of  the  incident 
rays,  which  are  polarized  perpendicularly  to  the  plane  of  in- 
cidence, the  body  reflects  less,  but  also  absorbs  more  than  it 
does  of  rays  whose  plane  of  polarization  is  the  plane  of  in- 
cidence. According  to  this  law  the  state  of  polarization  of  the 
rays  sent  out  may  easily  be  given  if  the  law  ot  the  reflection  of 
the  incident  rays  is  known. 

1  Phil.  Mag.  XXX.    p.  345  ;  Berl.    Ber.  1847. 

95 


MEMO in S     ON 

A  tourmaline  plate,  cut  parallel  to  the  optic  axis,  absorbs, 
at  ordinary  temperatures,  moraof  the  rays  which  strike  it  nor- 
mally, if  the  plane  of  polarization  of  these  is  parallel  to  the 
axis  than  when  it  is  perpendicular  to  it.  Assuming  that  the 
tourmaline  plate  retains  this  property  when  it  is  at  a  glowing 
heat,  it  must  give  out  rays  in  a  direction  normal  to  it,  which 
are  partially  polarized  in  the  plane  passing  through  the  optic 
axis  and  which  is  the  plane  perpendicular  to  that  which  is 
called  the  plane  of  polarization  of  the  tourmaline.  1  have 
proved  this  striking  deduction  from  theory  by  experiment  and 
it  confirmed  the  same.  The  tourmaline  plates  employed  with- 
stood a  considerable  temperature,  glowing  for  a  long  time  in 
the  flame  of  the  Bunsen  burner  without  undergoing  any  per- 
manent change;  only  after  cooling  did  they  appear  dull  at  the 
edges.  The  property  of  polarizing  transmitted  light  was 
retained  even  at  an  incandescence,  although  in  a  considerable 
less  degree  than  at  a  lower  temperature.  This  appeared  on 
observing,  through  a  double  refracting  prism,  a  platinum  wire 
made  incandescent  in  the  flame  and  placed  behind  a  tourma- 
line plate.  The  two  images  of  the  platinum  wire  were  of  un- 
equal brightness,  although  the  difference  was  much  less  than 
when  the  tourmaline  plate  was  outside  of  the  flame.  The 
double  refracting  prism  was  then  given  the  position  in  which 
the  difference  of  the  intensities  of  the  two  images  was  a  maxi- 
mum ;  suppose  the  upper  image  were  the  brighter ;  then,  after 
removal  of  the  platinum  wire  the  two  images  of  the  tourmaline 
plate  were  compared.  The  upper  image  was  not  strikingly, 
but,  unmistakably,  darkerthan  the  other;  both  images  appeared 
exactly  like  to  two  similar  incandescent  bodies,  of  which  the 
upper  had  a  less  temperature  than  the  lower  one. 

§17. 

Still  another  result  of  the  law  established  may,  in  conclusion, 
be  admitted  here.  When  a  space  is  surrounded  by  bodies  of 
the  same  temperature,  and  no  rays  can  penetrate  through  these 
bodies,  every  pencil  in  the  interior  of  the  space  is  so  consti- 
tuted, with  respect  to  its  quality  and  intensity,  as  if  it  pro- 
ceeded from  a  perfectly  black  body  of  the  same  temperature, 
and  is  therefore  independent  of  the  nature  and  form  of  the 

96 


RADIATION   AND   ABSORPTION. 

bodies,  and  only  determined  by  the  temperature.  The  truth 
of  this  statement  is  evident  if  we  consider  that  a  pencil  of  rays, 
which  has  the  same  form,  but  the  reverse  direction  to  that 
chosen,  is  completely  absorbed  by  the  infinite  number  of  reflec- 
tions which  it  successively  experiences  at  the  assumed  bodies. 
In  the  interior  of  an  opaque  glowing  hollow  body  of  given  tem- 
perature there  is,  consequently,  always  the  same  brightness 
whatever  its  nature  may  be  in  other  respects. 

BIOGRAPHICAL  SKETCH. 

GUSTAV  ROBERT  KIRCHHOFE,  the  son  of  Counselor-at-law 
Kirchhoff,  was  born  March  12,  1824,  at  Kdnigsberg.  He  took 
his  degree  of  doctor  of  philosophy  at  the  University  in  1847. 
The  following  year  he  became  private-docent  at  the  University 
of  Berlin.  He  early  showed  those  rare  mathematical  faculties 
which  later  distinguished  him.  As  early  as  his  eighteenth  year 
he  decided  upon  physics  as  the  branch  to  which  he  should 
devote  his  life's  work.  By  1845  he  had  investigated  electric 
currents,  and  established  the  two  so-called  Kirchhoff's  laws  for 
current  conduction.  Other  important  papers  on  electricity  fol- 
lowed in  rapid  order.  In  1854  he  was  called  to  Breslau,  where 
he  became  associated  with  Bunsen.  He  went  to  Heidelberg  in 
1854  where  Bunsen  had  preceded  him.  Here  in  his  prime  he 
wrought  and  sought  for  twenty  years,  and  in  connection  with 
Bunsen  achieved  some  of  the  most  important  discoveries  in  the 
history  of  physical  science.  In  1875  he  accepted,  after  twice 
declining  an  invitation  to  the  University,  a  call  to  the  chair  of 
theoretical  physics  at  Berlin  where  he  became  associated  with 
his  former  colleague  von  Helmholtz.  Here  he  delivered  for 
eleven  years  (with  serious  interruption  in  the  last  two  years)  his 
famous  courses  of  lectures  on  theoretical  physics.  It  is  during 
this  period  that  we  find  the  most  brilliant  aggregation  at  Berlin 
of  scholars  in  the  faculty  of  mathematics  and  physics  during 
the  century.  His  contributions  extend  over  optics,  heat,  fluid, 
motion,  electricity,  elasticity,  etc.,  and  all  bear  the  imprint  of 
the  great  genius  he  was.  He  died  unexpectedly  Oct.  17,  1887, 
after  many  months  of  disability.  His  papers  and  lectures 
have  been  collected  and  edited  and  now  form  one  of  the  endur 
ing  monuments  in  physical  science. 

97 


CHEMICAL  ANALYSIS  BY  SPECTRAL 
OBSERVATIONS. 

BY 

G.  KIRCHHOFF  AND  R.  BUNSEN". 

Poggendorf ',?  A  nnalen,  Band  1 10,  1 860  ;   Gesammelte  Abliand- 
lungen  von  G.  Kirclilioff.    pp.  598-625,  1882. 


99 


CONTENTS. 


PAGE 

Methods  of  Purifying  Salts 101 

Apparatus  described  .         .        .        .        .         .         .103 

Sodium         .        .        .         .          .         .         .         ,        .         .     107 

Lithium       .         .        . 109 

Potassium  .         .         .         .         .         .         .         .         .         .113 

Strontium,   .         . 113 

Calcium      .         .         .        .         .         .         .         .         .         .115 

Barium 119 

Advantage  of  Spectrum  Analysis  over  other  Methods  .         .    122 
Law  of  Reversed  Spectra      ...  .  123 


100 


CHEMICAL  ANALYSIS  BY  SPECTRAL 
OBSERVATIONS.1 

IT  is  well  known  that  many  substances  have  the  property 
when  they  are  brought  into  a  flame  of  producing  in  the  spec- 
trum certain  bright  lines.  We  can  found  on  these  lines  a 
method  of  qualitative  analysis  which  greatly  enlarges  the  field 
of  chemical  reactions  and  leads  to  the  solution  of  problems 
unsolved  heretofore.  We  shall  confine  ourselves  here  only  to 
the  extension  of  the  method  to  the  detection  of  the  metals  of 
the  alkalis  and  the  alkali  earth  and  to  the  illustration  of  their 
value  iii  a  series  of  examples. 

The  lines  referred  to  show  themselves  the  more  plainly,  the 
higher  the  temperature  and  the  weaker  the  natural  illuminating 
power  of  the  flame.  The  gas  lamp2  described  by  one  of  us 
gives  a  flame  of  very  high  temperature  and  very  small  luminosity; 
this  is  consequently  especially  adapted  to  investigations  on 
those  substances  characterized  by  bright  lines. 

In  Figure  1  the  spectra  are  represented  which  the  flames 
referred  to  give  when  the  salts,  as  pure  as  possible,  of  potassium, 
sodium,  lithium,  strontium,  calcium,  and  barium  are  vaporized 
in  it.  The  solar  spectrum  is  annexed  in  order  to  facilitate  the 
comparison. 

The  potassium  compound  used  for  the  investigation  was 
obtained  by  heating  chlorate  of  potassium  which  had  been  six  to 
eight  times  recrystallized  beforehand. 

The  chloride  of  sodium  was  obtained  by  combining  pure  car- 
bonate of  sodium  and  hydrochloric  acid  and  purifying  the  same 
by  repeated  crystallization. 

The  lithium  salt  was  purified  by  precipitating  fourteen  times 
with  carbonate  of  ammonium. 

For  the  production  of  the  calcium  salt  a  specimen  of  marble 


1  Kirchhoff  and  R.  Bnnsen,  Pogg.  Ami.  Vol.  110.  1860. 

2  Bunsen,  Fogg.  Ann.  Vol.  100  p.  85. 

101 


I1  &  &  S  %  M 


RADIATION   AND   ABSORPTION. 

as  pure  as  possible,  and  dissolved  in  hydrochloric  acid,  was 
used.  From  this  solution  the  carbonate  of  calcium  was  thrown 
down  by  a  fractional  precipitation  with  carbonate  of  ammonium 
in  two  portions,  of  which  only  the  latter,  precipitated  in  calcium 
nitrate,  was  used.  The  calcium  salt  thus  obtained  we  dissolved 
several  times  in  absolute  alcohol  and  converted  it  finally  into 
the  chloride  by  evaporating  the  alcohol  and  by  precipitation 
with  carbonate  of  ammonium  in  hydrochloric  acid. 

In  order  to  obtain  the  pure  chloride  of  barium  we  extracted  it 
from  the  commercial  salt  by  pulverizing  and  boiling  repeatedly 
in  nearly  absolute  alcohol.  The  residue  thus  extracted  and 
freed  from  alcohol  was  dissolved  in  water  and  thrown  down  by 
fractional  precipitation  in  two  portions,  only  the  second  being 
dissolved  in  hydrochloric  acid,  and  the  barium  chloride  thus 
obtained  being  further  purified  by  repeated  crystallizations. 

In  order  to  obtain  chloride  of  strontium,  as  pure  as  possible, 
the  commercial  salt  was  crystallized  out  from  alcohol,  and  frac- 
tionally precipitated  in  two  portions  with  carbonate  of  ammon- 
ium, the  second  part  being  dissolved  in  nitric  acid  and  the  ni- 
trate freed  from  the  last  traces  of  calcium  by  pulverizing  and 
boiling  with  alcohol.  From  the  product  thus  purified  the  chlo- 
ride of  strontium  was  obtained  finally  by  precipitating  with 
carbonate  of  ammonium  and  dissolving  the  precipitate  in 
hydrochloric  acid.  All  these  purifications  were  made  in  plat- 
inum vessels  as  far  as  it  was  possible. 

Figure  2    represents    the    apparatus  which    we   have    used 

mainly  in  the  observation 
of  the  spectra.  A  is  a 
box  blackened  on  the  in- 
side the  bottom  of  which 
has  the  form  of  a  trapez- 
ium and  rests  on  three 
feet ;  the  two  inclined 
sides  of  the  same  form  an 

FIG  2  angle  with  one  another  of 

about  58°  and  carry  the 

two  small  telescopes  B  and  C.  The  ocular  of  the  first  is  removed 
and  replaced  by  a  plate  in  which  is  a  slit  formed  of  two  brass 
cheeks  which  are  placed  at  the  focus  of  the  objective.  The 

103 


MEMOIRS     ON 

lamp  D  is  so  placed  before  the  slit  that  the  mantle  of  the  frame 
is  intersected  by  the  axis  of  the  tube  B.  Somewhat  beneath 
the  point  where  the  axis  meets  the  mantle  the  end  of  a  very  fine 
platinum  wire  bent  into  a  small  hook  and  carried  by  the  holder 
E  passes  into  the  same;  on  this  hook  is  melted  a  globule  of  the 
chloride  previously  dried.  Between  the  objective  of  the  tele- 
scopes B  and  C  is  placed  a  hollow  prism  F  with  a  reflecting 
angle  of  60°  and  filled  with  carbon  disulphide.  The  prism 
rests  on  a  brass  plate  which  can  be  rotated  on  a  vertical  axis. 
This  axis  carries  on  its  lower  end  the  mirror  G  and  above  it 
the  arm  //which  serves  as  the  handle  to  rotate  the  prism  and 
the  mirror.  A  small  telescope  is  adjusted  before  the  mirror 
which  gives  an  image  of  a  horizontal  scale  placed  at  a  short  dis- 
tance. By  rotating  the  prism  we  can  cause  to  pass  before  the 
vertical  thread  of  the  telescope  C  the  entire  spectrum  of  the 
flame  and  bring  every  portion  of  the  spectrum  into  coincidence 
with  this  thread.  To  every  reading  made  on  the  scale  there 
corresponds  a  particular  portion  of  the  spectrum.  If  the  spec- 
trum is  very  weak  the  cross  hair  of  the  telescope  C  is  illumi- 
nated by  means  of  a  lens  which  throws  some  of  the  rays  from  a 
lamp  through  a  small  opening  which  is  placed  laterally  in  the 
ocular  of  the  telescope  C. 

The  spectra  in  Fig.  1.  obtained  by  means  of  the  pure  chlo- 
ride above  mentioned  we  have  compared  with  those  which  we 
obtained  if  we  introduce  the  bromides,  iodides,  hyd rated  oxides, 
sulphates,  and  carbonates  of  the  several  metals  into  the  follow- 
ing flames: — 

into  the  flame  of  sulphur, 

"       "      "       "   carbon  disulphide, 

"      "      "       "   aqueous   alcohol, 

"      "  non-luminous  flame  of  coal  gas, 

"      "  flame  of  carbonic  oxide, 

"      "      "       "   hydrogen  and 

"       "  oxyhydrogen  flame. 

From  these  comprehensive  and  lengthy  investigations  whose 
details  we  may  be  permitted  to  omit,  it  appears  that  the  dif- 
ference in  the  combinations  in  which  the  metals  were  used,  the 
multiplicity  of  the  chemical  processes  in  the  several  flames,  and 
the  enormous  differences  of  temperatures  of  the  latter  exert  no 
influence  on  the  position  of  the  spectral  lines  corresponding  to  the 
individual  metals. 

104 


RADIATION  AND  ABSORPTION. 


How  considerable  the  differences  of  temperature  mentioned 
are,  is  shown  by  the  following  treatment. 

We  may   arrive   at   an   approximation   of   temperature  of  a 

flame  by  means  of  the  equation   t  =   -?~,  in  which  t  is  the 

temperature  of  the  flame  sought,  g  the  weight  of  the  substance 
burning  in  oxygen,  w  the  heat  of  combustion  of  the  same,  p  the 
weight  and  s  the  specific  heat  of  one  of  the  products  of  combus- 
tion. 

If  we  take  as  the  heat  of  combustion 

of  sulphur as  2240°  C 


3400 
34462 
13063 
11640 
11529 

2403 


'  carbon  disulphide 

'  hydrogen 

'  marsh  gas 

'  elayle 

*  ditetryle 

'  carbonic  oxide 

and  place  according  to  Regnault  the  specific  heat  at  constant 

pressure 

for  sulphurous  acid =0. 1553 

"  carbonic  acid =0.2164 

"  nitrogen =0.2440 

"  aqueous  vapor  =0.4750 

we  find  accordingly  the  temperature 

of  the  sulphur  flame 1820°  C 

'  bisulphide  of  carbon  flame.... 2195 

'  coal  gas  flame1 2350 

'  carbonic  oxide  flame2 3042 

'  hydrogen  flame  in  air3 3259 

'  oxyhydrogen  flame4 8061. 

It  appears  that  the  same  metal  compound  gives  in  one  of 
these  flames  a  spectrum  as  much  more  intense  as  the  tempera- 
ture is  higher.  Of  the  compounds  of  these  metals,  those  give 
the  greatest  intensity  in  a  flame  which  have  the  greatest 
volatility. 

In  order  to  obtain  a  further  proof  that  each  of  the  severally 
mentioned  metals  always  give  the  same  bright  lines  in  the 
spectrum,  we  have  compared  the  spectra  referred  to  with  those 


1  Liebig's  Ann.     Vol.  CXI.  p.  258 

8  Gasometric  Methods  by  R.  Bunsen.  p.  254. 

3  Ibid. 

4  Ibid. 


105 


MEMOIKS     OK 

which  an  electric  spark  produces  which  passes  between 
electrodes  made  from  these  metals. 

Small  pieces  of  potassium,  sodium,  lithium,  strontium,  and 
calcium  were  fastened  on  a  fine  platinum  wire  and  so  melted  in 
pairs  within  glass  tubes  that  they  were  separated  by  a  distance 
of  1  to  2mm  from  one  another  the  wires  piercing  the  sides  of 
the  tubes.  Each  of  these  tubes  was  placed  before  the  slit  of 
the  spectroscope  ;  by  means  of  a  Bnhmkorff's  induction 
apparatus,  we  caused  electric  sparks  to  pass  between  the  metal 
pieces  mentioned  and  compared  the  spectrum  of  the  same  with 
the  spectrum  of  a  gas  flame  in  which  the  chloride  of  the  cor- 
responding metal  was  brought.  The  flame  was  placed  behind 
the  glass  tube.  When  the  Ruhmkorff  apparatus  was  thrown 
alternately  in  and  out  of  action  it  was  easy  to  be  convinced, 
without  any  accurate  measurement,  that,  in  the  brilliant  spec- 
trum of  the  spark,  the  bright  lines  of  thespectrnmof  the  flame 
were  present  undisplaced.  In  addition  to  these  there  appeared 
other  bright  lines  in  the  spark  spectrum  a  part  of  which  must 
be  attributed  to  the  presence  of  foreign  metals  in  the  electrodes, 
others  to  nitrogen  which  filled  the  tubes  after  the  oxygen  had 
partly  oxidized  the  electrodes.1 

It  appears,  accordingly,  beyond  a  question  that  the  bright 
lines  of  the  spectra  indicated  maybe  considered  as  certain  proof 
of  the  presence  of  the  metal  in  consideration.  They  can  serve 
as  reactions  by  means  of  which  this  material  may  be  detected 
more  certainly,  and  quickly  and  in  smaller  quantities  than  by 
any  other  analytical  method. 

The  spectra,  represented,  refer  to  the  case  when  the  slit  is 
wide  enough  so  that  only  the  most  prominent  of  the  dark  lines 
of  the  solar  spectrum  are  visible,  the  magnifying  power  of  the 
observing  telescope  being  small  (about  four-fold)  and  the 
intensity  of  the  light  moderate.  These  conditions  seem  to  us 

1  In  one  investigation  with  strontium  electrodes  we  used  a  tube  filled 
with  hydrogen  instead  of  nitrogen,  and  the  stream  of  sparks  was  trans- 
formed very  soon  into  an  arc,  while  the  sides  of  the  tuhe  were  covered 
with  a  gray  precipitate.  On  opening  the  tube  nnder  rock-oil  it  appeared 
that  the  hydrogen  had  vanished  and  a  vacuum  existed.  The  gns 
appears,  therefore,  at  the  enormous  temperature  of  the  electric  spark,  to 
have  dissociated  the  strontium  oxide  which  had  not  been  completely 
removed  from  the  surface  of  the  metal. 

106 


RADIATION  AND  ABSORPTION. 

most  advantageous  when  it  is  necessary  to  carry  out  a  chemical 
analysis  by  spectral  observations.  The  appearance  of  the 
spectrum  may  under  other  conditions  be  quite  different.  If  the 
purity  of  the  spectrum  is  increased,  many  of  the  lines  appearing 
as  single,  resolve  themselves  into  several,  the  sodium  line,  for 
example,  into  two  ;  if  the  intensity  is  increased  new  lines  appear 
in  many  of  the  spectra  shown  and  the  relation  of  the  brightness 
of  the  old  ones  becomes  different.  In  general  the  brightness  of 
a  darker  line  increases  with  greater  luminosity  more  rapidly 
than  the  brighter  ones,but  not  so  much  that  the  former  exceed 
these.  A  clear  example  of  this  is  given  by  the  two  lithium 
lines.  We  have  observed  only  one  exception  to  this  rule, 
namely,  with  the  line  Ba  ?,  which,  with  low  luminosity,  is 
barely  visible  while  Zto^appears  very  distinct,  and,  with  greater 
luminosity,  much  brighter  than  the  former.  This  fact  appears 
of  importance,  and  we  shall  make  a  further  study  of  the  same. 
We  will  now  consider  more  closely  the  characteristics  of  the 
several  spectra,  the  knowledge  of  which  is  of  importance  from 
a  practical  standpoint,  and  indicate  the  advantage  which  the 
chemical  analytical  method  founded  upon  it  furnishes. 

SODIUM. 

Of  all  the  spectral  reactions  that  of  sodium  is  the  most  sen- 
sitive. The  yellow  line  Na  a,  the  only  one  which  is  shown  in 
the  sodium  spectrum  coincides  with  Fraunhofer's  line  D  and  is 
characterized  by  its  peculiarly  sharp  boundary  and  its  extraor- 
dinary brilliancy.  If  the  temperature  of  the  flame  is  very  high 
and  the  quantity  of  the  substance  used  very  great,  traces  of  a 
continuous  spectrum  are  seen  in  the  immediate  neighborhood 
of  the  line.  Lines  of  other  substances,  in  themselves  very 
weak,  lying  near  it  appear  still  weak  and  will,  therefore,  often 
first  be  visible  after  the  sodium  reaction  has  begun  to  disappear. 

In  the  oxygen,  chlorine,  iodine  and  bromine  compounds  in 
sulphuric  acid  and  carbonic  acid  the  reaction  is  most  evident. 
But  it  is  present  also  in  the  silicates,  borates,  phosphates  and 
other  non -volatile  salts. 

Swani  has  already  called  attention  to  the  minuteness  ef  the 

1  Pogg.  Arm.  Vol.  C,  p.  311. 

107 


MEMOIRS     ON 

quantity  of  common  salt  which  can  produce  the  sodium  line 
clearly. 

The  following  investigation  shows  that  chemistry  produces 
no  single  reaction  which  in  the  remotest  degree  can  compare  in 
sensitiveness  with  this  analytical  spectral  determination  of 
sodium.  We  detonized  in  one  corner  of  the  experiment  room 
which  contained  about  60  cubic  meters  of  air  and  as  far  as 
possible  from  our  apparatus  three  milligrams  of  chlorate  of 
sodium  with  milk  sugar  while  the  non-luminous  flame  was 
observed  before  the  slit.  After  some  minutes,  the  flame,  becom- 
ing gradually  colored  pale  yellow,  gave  a  strong  sodium  line, 
which,  after  ten  minutes,  again  completely  vanished.  From  the 
weight  of  the  detonized  salt  and  the  air  contained  in  the  room 
it  is  easy  to  calculate  that  in  a  unit  weight  of  the  latter  not  a 
?oWr<rzrr>kh  part  of  sodium  smoke  could  have  been  suspended. 
As  the  reaction  can  be  readily  observed  in  a  second,  and  as,  in 
this  time,  according  to  the  rate  of  flow  and  the  composition 
of  the  gases  in  the  flame,  onty  about  50  ccm  or  0.0647  grams  of 
air  which  contained  less  than  ^otfoWoirth  of  sodium  salt,  reach 
the  state  of  incandescence  in  the  flame,  it  follows  that  the  eye 
is  capable  of  detecting  less  than  ^ootrotfth  °f  a  milligram  of 
sodium  salt  with  the  greatest  distinctness.  With  such  a  sen- 
sibility of  the  reaction  it  is  evident  that  only  rarely  is  a  sodium 
reaction  not  visible  in  glowing  atmospheric  air.  The  earth  is 
covered  over  more  than  two-thirds  of  its  surface  with  a  solu- 
tion of  chloride  of  sodium,  which,  by  the  waves  breaking  into 
foam,  is  transformed  continually  into  spray;  the  particles  of 
sea-water,  which  reach  the  atmosphere  in  this  way,  evaporate 
and  leave  behind  them  motes  of  salt  which  vary  in  magnitude, 
but,  as  it  appears,  are  rarely  absent  from  the  atmosphere,  and, 
perhaps,  serve  to  supply  the  small  organisms  the  salt  which  the 
larger  plants  and  animals  secure  from  the  ground.  The 
presence  in  the  air  of  salt,  easily  shown  by  spectral  analysis,  is 
yet  of  interest  from  another  standpoint.  If,  as  we  yet  can 
scarcely  doubt,  there  are  catalytic  influences  which  are  the 
cause  of  the  miasmic  spread  of  disease,  it  is  possible  that  an 
antiseptic  substance,  such  as  salt,  even  in  vanishingly  small 
quantities,  may  indeed  not  be  without  definite  influence  upon 
such  processes  in  the  air.  From  daily  and  long  continued 

108 


RADIATION  AND  ABSORPTION. 

spectrum  observation  it  would  be  easy  to  learn  whether  the 
variation  in  the  intensity  of  the  spectral  line  Ncta,  produced  by 
the  sodium  combination  in  the  air,  is  related  in  any  degree  to 
the  appearance  and  the  spread  of  endemic  diseases. 

In  the  exceedingly  delicate  sodium  reaction  may  also  be 
sought  the  reason  why  all  bodies  exposed  to  the  air  show  the 
sodium  line  after  a  time  when  heated  in  the  flame,  and  why  it 
is  possible  with  only  a  few  compounds  to  eliminate  the  last 
trace  of  the  sodium  line  No,  a  by  crystallizing  it  out  ten  or  more 
times  from  water  which  has  come  in  contact  with  platinum 
vessels  only.  A  hair  wire  of  platinum,  which  has  been  freed, 
by  heating,  from  every  trace  of  sodium,  shows  the  reaction 
most  vividly  again,  if  it  is  exposed  some  hours  to  the  air.  Dust 
which  settles  in  the  room  from  the  air  shows  it  in  the  same 
degree,  so  that,  for  example,  the  slapping  of  a  dusty  book  is 
quite  sufficient  to  produce  at  a  distance  of  several  spaces  the 
most  brilliant  flashes  of  the  No,  a  line. 

LITHIUM. 

The  incandescent  vapors  of  the  lithium  compound  give  two 
sharply  defined  lines,  one  a  very  weak  yellow  Li (3  and  a  red 
brilliant  line  Li  a.  In  certainty  and  delicacy  this  reaction  ex- 
ceeds all  those  known  heretofore  in  analytical  chemistry.  It 
approximates  in  sensibility  that  of  the  sodium  reaction  perhaps 
because  the  eye  is  more  sensitive  for  yellow  rays  than  for  re'd.  On 
detonizing  nine  milligrams  of  carbonate  of  lithium  with  a  large 
excess  of  milk  sugar  and  potassium  chlorate  in  the  room  which 
contained  about  60  cubic  meters  of  air,  the  line  became  quite 
evident.  The  eye  can  therefore  in  this  way,  as  a  calculation 
similar  to  the  one  made  above  will  show,  perceive  less  than 
T¥_jTFTTTTth  of  a  milligram  of  carbonate  of  lithium  with  the 
greatest  distinctness.  0.05  grams  of  the  same  salt,  detonized  in 
the  way  already  mentioned,  made  it  possible  to  observe  the  Li  a 
line  in  the  air  of  the  same  room  during  more  than  an  hour. 

The  oxygen,  chlorine,  iodine  and  bromine  compounds  are 
most  suitable  for  observing  lithium.  But  the  carbonate,  sul- 
phate, and  even  phosphate  are  almost  as  well  suited  for  this 
purpose.  Minerals  containing  lithium,  as  triphyllin,  triphan, 
petalit,  lepidolith,  need  only  to  be  held  in  the  flame  in  order 

109 


MEMOIRS    ON 

to  give  the  line  Li  a  with  an  intense  lustre.  In  this  way  it  is 
possible  to  show  the  presence  of  lithium  in  many  f eld -spars, 
for  example  in  orthoclase  from  Baveno.  The  line  is  seen  only 
momentarily  immediately  after  the  insertion  of  the  specimen  in 
the  flame.  Thus  mica  from  Altenberg  and  Penig  indicates  the 
presence  of  lithium  while  on  the  contrary  mica  from  Miask, 
Ashaffenburg,  Modum,  Bengal,  Pennsylvania,  etc.,  is  free  from 
lithium.  When  in  naturally  deposited  silicates  only  a  vanish- 
ingly  small  quantity  of  lithium  is  present,  it  escapes  immediate 
observation.  The  test  in  such  cases  is  then  best  made  in  the 
following  way:  we  digest  and  evaporate  a  small  quantity  of  the 
substance  for  examination  with  hydrofluoric  acid  or  fluoride  of 
ammonium,  moisten  the  remainder  with  sulphuric  acid,  and 
dissolve  the  dry  mass  with  absolute  alcohol.  The  alcoholic 
solution  is  then  evaporated  to  dryness,  again  dissolved  with 
alcohol,  and  the  fluid,  thus  obtained,  evaporated  in  as  shallow  a 
dish  as  possible.  The  product  which  remains  can  be  easily 
scraped  together  by  means  of  an  erasing  knife  and  brought  into 
the  flame  on  platinum  wire,  i^th  of  a  milligram  of  the  same  is 
usually  quite  sufficient  for  the  experiment.  Other  compounds 
than  the  silicates,  in  which  we  may  wish  to  detect  the  least 
traces  of  lithium,  maybe  transformed  into  sulphates  by  evapo- 
ration with  sulphuric  acid  or  in  any  other  way  and  then  treated 
as  above. 

By  means  of  these  experiments,  the  unanticipated  conclusion 
is  readily  drawn  that  lithium  belongs  to  those  substances  which 
are  most  widely  distributed  in  nature.  This  is  easily  shown  by 
means  of  40  cubic  centimeters  of  sea-water  which  was  collected 
in  the  Atlantic  ocean  in  latitude  41°  41'  and  longitude  39°  14'. 
Ashes  of  Fucoids  (kelp)  which  was  driven  on  to  the  Scottish 
coast  from  the  Gulf  Stream  contained  appreciable  traces  of  it. 
All  orthoclase  and  quartz  from  the  granite  of  the  Oldenwald 
which  we  have  tested  show  a  lithium  content.  A  very  pure 
drinking  water  from  a  spring  on  the  western  granitic  declivity 
of  the  Neckar  valley  in  Schlierbach  near  Heidelberg  contained 
lithium,  while  the  spring  rising  in  the  red  sandstone  which 
supplies  the  water  pipes  of  this  chemical  laboratory  was  free 
from  it.  Mineral  water,  in  a  litre  of  which  lithium  can 
scarcely  be  detected  by  the  ordinary  analytical  methods,  shows 

110 


RADIATION  AND  ABSORPTION. 

the  Li  a  line  frequently  if  we  put  a  drop  of  the  same  into  the 
flame  on  a  platinum  wire.1  All  the  ashes  of  woods  in  the  Olden- 
wald  which  grow  on  granite  soil,  as  well  as  Russian  and 
other  commercial  potashes  examined  by  us,  contain  lithium. 
Neither,  even,  in  the  ashes  of  tobacco,  vine  leaves,  vine-wood 
and  grapes,'2  as  well  as  in  the  ashes  of  crops  which  were  culti- 
vated in  the  Rhine  plain  near  Waghausel,  Deidesheim  and 
Heidelberg  on  non-granitic  earth,  was  lithium  lacking,  nor  in 
the  milk  of  the  animals  which  were  fed  upon  these  crops.3 

It  will  be  scarcely  necessary  to  remark  that  a  mixture  of 
volatile  sodium  and  lithium  salts  shows,  along  with  the  reaction 
of  sodium,  that  of  lithium  with  a  scarcely  less  preceptible  sharp- 
ness and  distinctness.  The  red  line  of  the  last  appears  still 
quite  distinct  when  a  small  bead  containing  the  y^^th  part  of 
lithium  salts  is  introduced  into  the  flame,  where  the  eye, 
unaided,  perceives  in  the  same,  nothing  more  than  yellow 
light  of  sodium  without  any  indication  of  red  coloration.  On 
account  of  the  greater  volatility  of  lithium  salts,  the  sodium 
reaction  lasts  somewhat  longer.  When,  therefore,  it  is  desired 
to  detect  very  small  traces  of  lithium  along  with  sodium,  the 
bead  for  testing  must  be  introduced  into  the  flame  whilst  we 
are  observing  through  the  telescope.  We  then  often  observe 
the  lithium  line  only  for  a  few  moments  during  the  first 
products  of  volatilization. 

In  the  production  of  lithium  compounds  on  a  commercial 
scale  spectrum  analysis  is  a  means  of  inestimable  value  in  the 
selection  of  the  raw  material  used  and  the  determination  of  an 
efficient  method  of  manufacture.  Thus  for  example,  it  is  only 
necessary  to  evaporate  a  drop  of  the  different  mother-liquors  in 

1  When  it  is  required  to  introduce  a  liquid  into  the  flame  we  bend  in 
the  end  of  a  horse-hair  platinum  wire,  a  ring  of  suitable  diameter  and 
hammer  the  same  flat.     If  we  let  a  drop  of  the  fluid  fall  into  the  ring 
thus  formed  a  sufficient  quantity  for  the  investigation  remains  hanging 
within. 

2  Lithium  is  concentrated  so  much  in  the  mother-liquors  in  the  man- 
ufacture of  tartaric  acid  that  we  can  obtain  considerable  quantities  from 
them. 

3  Dr.  Folwarcznyhas  even  been  able  to  show  with  the  lithium  line  Li  a 
the  lithium   compounds  in  the  ash  of  human  blood  and   of   muscular 
tissue. 

Ill 


MEMOIKS     ON 

the  flame  and  observe  through  the  telescope,  in  order  to  show 
at  once,  that,  in  many  of  these  saline  residues,  a  rich  and 
hitherto  overlooked  lithium  source  exists.  Thus  in  the  process 
of  preparation,  we  can  follow  any  loss  of  lithium  in  the  as- 
sociated products  and  wastes  by  means  of  the  spectral  reaction, 
and  thus  easily  seek  more  efficient  methods  of  production  than 
those  heretofore  used.1 

POTASSIUM. 

The  volatile  potassium  compounds  produce  in  the  flame  a 
very  extended  continuous  spectrum  which  only  show  two 
characteristic  lines  ;  the  first  K  a,  in  the  outermost  red  border- 
ing on  the  ultra  red  rays  falls  exactly  on  the  dark  line  A  of  the 
solar  spectrum;  the  second  K  $  far  in  the  violet  toward  the 
other  end  of  the  spectrum,  corresponds  likewise  to  a  Fraunhofer's 
line.  A  very  weak  line,  coinciding  with  the  Fraunhofer's  line 
B,  which,  however,  is  only  visible  with  an  intense  flame,  is  less 
characteristic.  The  blue  line  is  somewhat  weak  but  is  almost  as 
well  suited  for  detecting  potassium  as  the  red  line.  The  position 
of  both  lines,  in  the  neighborhood  of  the  limits  of  the  rays  per- 
ceptible by  the  eye,  renders  the  reaction  somewhat  less  sensitive. 

In  the  air  of  our  room  it  became  first  visible  when  we  burned 
about  one  gram  of  chlorate  of  potassium  mixed  with  milk 
sugar.  We  can,  therefore,  make  clear  to  the  eye  in  this  way 
about  -nnr^h  of  a  milligram  of  chlorate  of  potassium. 

Potassium  hydrate  and  all  compounds  of  potassium  with 
volatile  acids,  show  the  reaction  without  exception.  Potassium 
silicate  and  similar  non-volatile  salts,  on  the  contrary,  produce 
it  only  when  the  potassium  is  present  in  large  quantities. 
With  small  amounts,  the  test  bead  may  be  melted  together 
with  some  carbonate  of  sodium  in  order  to  make  the  char- 
acteristic lines  visible.  The  presence  of  the  sodium  does  not 
prevent  the  reaction  and  hardly  affects  the  sensibility.  Ortho- 


1  We  obtained  by  such  an  approved  method  from  two  jars  of  mineral 
water  (about  four  litres)  a  mother-water,  which  gave  on  evaporation 
with  sulphuric  acid  a  residue  of  1.2  K,  half  an  ounce  of  carbonate  of 
lithium  of  the  purity  of  the  commercial,  whose  cost  would  be  about 
140  fl.  per  pound.  A  great  number  of  other  mother-waters  which  we 
examined  showed  a  like  wealth  iu  lithium  compounds. 

112 


RADIATION   AND   ABSORPTION. 

clase,  sanidine,  and  adularia  may  easily  be  distinguished  in 
this  way  from  albite,  oligoclase,  Labradorite,  and  anorthite. 
In  order  to  detect  traces  of  potassium,  vaiiishingly  small,  we 
need  to  heat  to  a  feeble  incandescence  the  silicate,  with  a  large 
excess  of  fluoride  of  ammonium,  in  a  platinum  crucible  and  in- 
troduce the  residue  into  the  flame  on  a  platinum  wire.  In  this 
way  we  find  that  almost  every  silicate  contains  potassium. 
The  lithium  salts  disturb  the  reaction  but  little.  Thus,  for 
example,  it  is  only  necessary  to  hold  the  ash  end  of  a  cigar  in 
the  flame  before  the  slit,  in  order  to  produce  at  once  very  dis- 
tinctly the  yellow  line  of  the  sodium  and  the  two  red  ones  of 
potassium  and  lithium,  the  last  metal  being  scarcely  ever 
absent  in  tobacco  ash. 

STRONTIUM. 

The  spectra  of  the  alkali  earths  are  not  so  simple  as  those  of 
the  alkalis.  That  of  strontium  is  characterized,  particularly,  by 
the  absence  of  green  bands.  Eight  lines  of  the  same  are  quite  re- 
markable namely  six  red,  one  orange  and  one  blue.  The  orange 
line  Sr  a  which  appears  close  to  the  sodium  line  toward  the  red, 
the  two  red  lines  Srp,  Sr  y  and  finally  the  blue  line  Sr  6  are  the 
most  important  in  their  position  and  intensity.  In  order  to 
test  the  sensibility  of  the  reaction  we  heated  quickly  in  a  plat- 
inum dish,  over  a  large  flame,  an  aqueous  solution  of  chloride 
of  strontium  of  known  concentration  until  the  water  was 
evaporated  and  the  dish  began  to  glow.  The  salt  then  began  to 
decrepitate  into  microscopic  particles  which  were  thrown  into 
the  air  in  the  form  of  white  smoke.  A  weighing  of  the  salt 
residue  in  the  dish  showed  that  in  this  way  0.077  grams  of 
chloride  of  strontium  had  passed  out  into  the  77,000  grams' 
weight  of  air  of  the  room  in  form  of  a  fine  dust.  After  the  air 
of  the  room  had  been  thoroughly  mixed,  by  means  of  an  open 
umbrella  moved  rapidly  about,  the  characteristic  lines  of  the 
strontium  spectrum  were  very  beautifully  outlined.  We  can  ac- 
cording to  this  experiment  estimate  the  amount  of  chloride  of 
strontium  preceptible  at  TWWfcn  °f  a  milligram. 

The  chlorine  and  the  other  haloid  compounds  of  strontium 
give  the  most  distinct  reaction.  Strontium  hydrate  and  carbon- 
ate of  strontium  show  them  much  more  feebly;  the  sulphate 

113 


MEM  OIKS    ON 

still  less  distinctly;  the  compounds,  with  the  non-volatile 
acids,  the  weakest  or  not  at  all.  We  must  therefore  introduce 
into  the  flame,  first,  the  bead  for  testing  by  itself,  and  then 
again,  after  previously  moistening  with  hydrochloric  acid.  If 
we  assume  sulphuric  acid  in  the  bead,  we  must  hold  it  some 
moments  in  the  reducing  part  of  the  flame  before  moistening 
with  hydrochloric  acid,  in  order  to  transform  the  sulphate  into 
the  sulphide  which  is  decomposed  by  hydrochloric  acid.  To 
detect  strontium  in  compounds  of  silicic,  phosphoric,  boracic 
or  other  non-volatile  acids  we  proceed  best  in  the  following 
manner:  for  fusing  with  carbonate  of  sodium  a  conical  spiral 
of  platinum  wire  is  used  instead  of  a  platinum  crucible.  The 
same  is  made  white  hot  in  the  flame  and  dipped  into  dry  fine 
pulverized  carbonate  of  sodium  which,  when  possible,  contains 
enough  water  so  that  the  necessary  quantity  of  the  salt  remains 
hanging  to  the  same  on  the  first  immersion.  Fusion  can  be 
effected  in  this  spiral  much  quicker  than  in  the  platinum 
crucible,  since  the  mass  of  the  platinum  heated  is  small  and 
the  salt  to  be  fused  comes  into  immediate  contact  with  the 
flame.  If  we  transform  the  fine  pulverized  substance  to  be 
tested  into  the  glowing  fluid  soda  by  means  of  a  small  plat- 
inum spatula,  and  maintain  it  in  a  glowing  state  for  a  few 
minutes,  we  need  only  to  knock  the  spiral,  inverted  with  its 
vertex  upward,  on  the  edge  of  the  lamp  stand  in  order  to 
obtain  the  contents  of  the  same  in  the  form  of  a  large  solidified 
bead.  Wo  then  cover  the  bead  with  a  sheet  of  writing  paper 
and  press  it  by  means  of  an  elastic  knife  blade,  which  we  also 
use  after  removing  the  paper,  in  order  to  reduce  the  mass  still 
farther  to  the  finest  powder.  This  is  collected  on  the  edge  of 
a  plate  slightly  tilted  and  carefully  covered  with  hot  water 
which  is  allowed  to  flow  backwards  and  forwards  over  the  sub- 
stance, heaped  up  by  gentle  tipping  of  the  plate  and  finally, 
the  fluid,  remaining  over  the  sediment,  is  decanted.  It  is  easy, 
by  repeated  heating  of  the  plate,  to  draw  off  the  soluble  salt 
after  several  repetitions  of  this  process  without  stirring  up  the 
sediment  and  losing  an  appreciable  amount  of  the  same.  If 
instead  of  water  we  use  a  common  salt  solution,  the  operation 
may  be  conducted  more  quickly  and  certainly.  The  residue 
contains  the  strontium  as  carbonate,  of  which  a  few  tenths  of  a 

114 


RADIATION    AND    ABSOBPTION. 

milligram,  moistened  with  a  little  hydrochloric  acid  on  a  plat- 
inum wire,  give  a  brilliant  reaction.  In  this  way,  without 
platinum  crucible,  mortar,  evaporating  dish,  and  without 
funnel  and  filter,  it  is  possible  to  carry  out,  in  a  few  minutes, 
all  the  necessary  operations  of  fusing,  powdering,  digesting 
and  washing. 

The  reaction  of  potassium  and  sodium  is  not  affected  by  the 
presence  of  strontium.  The  lithium  reaction  takes  place  along 
with  the  three  mentioned  with  perfect  distinctness,  if  the 
quantity  of  lithium  is  not  too  small  with  respect  to  that  of  the 
strontium.  The  lithium  line  Li  a  then  appears  as  a  narrow  in- 
tensely red  and  sharply  defined  band  upon  the  weaker  red 
background  of  the  broad  strontium  band  Sr  p. 

CALCIUM. 

The  spectrum  of  calcium  can  be  immediately  distinguished  at 
the  first  observation  from  the  four  spectra  already  considered 
in  that  a  very  characteristic  and  intense  line  Ca  ft  is  present  in 
the  green.  Also  a  second  not  less  characteristic  feature  is  the 
very  brilliant  orange  line  Ca  a  which  lies  considerably  farther 
toward  the  red  end  of  the  spectrum  than  the  sodium  line  Naa 
and  the  orange  line  of  strontium  Sr  a.  By  burning  a  mixture 
of  calcium  chloride,  chlorate  of  potassium  and  milk  sugar  we 
obtain  a  smoke  whose  reaction  is  approximately  of  the  same 
sensibility  as  that  of  the  fumes  from  the  chloride  of  strontium 
under  the  same  conditions.  It  follows  from  an  examination 
made  in  this  way  that  T<yo6(nnj-  of  a  milligram  of  calcium  chlo- 
ride can  be  detected  easily  and  with  absolute  certainty.  Only 
the  calcium  compounds,  volatilized  in  the  flame,  show  this  re- 
action, and  the  more  volatile  they  are  the  more  distinct  it  is. 
Chloride  of  calcium,  iodide  of  calcium,  and  bromide  of  calcium 
are  best  in  this  respect.  Sulphate  of  calcium  gives  a  spectrum 
only  after  it  has  become  basic  but  then  very  brilliantly  and 
long  continued.  In  the  same  way  the  reaction  of  the  carbonate 
becomes  distinct  after  the  acid  has  been  driven  off. 

Compounds  of  calcium  with  non-volatile  acids  remain  indif- 
ferent in  the  flame,  but  if  they  are  attacked  by  hydrochloric 
acid,  the  reaction  may  be  easily  obtained  in  the  following  way: 

115 


MEMOIKS     ON 

we  introduce  a  few  milligrams,  or  perhaps  only  a  few  tenths  of 
a  milligram,  of  the  finely  pulverized  substance  on  the  flat  plat- 
inum ring,  somewhat  moistened,  into  the  less  heated  portion  of 
the  flame  until  the  powder  is  frittered  without  being  melted. 
If  we  allow  a  drop  of  hydrochloric  acid  to  fall  on  the  ring  the 
greater  part  of  it  will  remain  hanging.  If  we  pass  this  drop 
before  the  slit  of  the  spectroscope  into  the  hottest  part  of  the 
flame  it  volatilizes  without  boiling  on  account  of  its  spheroidal 
condition.  If  during  the  volatilizing  of  the  drop  we  look  into 
the  telescope  there  appears  at  the  instant  when  the  last  portion 
of  the  fluid  has  been  evaporated  a  brilliant  calcium  spectrum- 
which  flashes  out  but  for  a  moment  with  a  small  amount,  but 
continues  a  longer  or  a  shorter  time  with  considerable  quan- 
tities of  metal. 

Only  in  silicates  which  are  attacked  by  hydrochloric  acid  can 
the  calcium  be  found  in  this  way;  in  silicates  which  are  not 
attacked  by  hydrochloric  acid  the  test  is  best  obtained  in  the 
following  way: — a  few  milligrams  of  the  substance  to  be  tested 
are  pulverized  as  fine  as  possible  and  placed  on  a  flat  platinum 
crucible  cover  with  about  a  gram  of  half-dissolved  fluoride  of 
ammonium  and  the  cover  held  in  the  flame  until  it  volatilizes 
the  fluoride  of  ammonium.  We  moisten  the  salt  residue  re- 
maining on  the  cover  with  one  to  two  drops  of  sulphuric  acid, 
and  drive  off  the  excess  of  the  same  by  gently  heating  over  the 
flame.  If  the  residue  of  the  sulphates  now  remaining  on  the 
cover  be  scraped  together  with  the  finger-nail  or  a  spatula  and 
about  a  milligram  of  the  same  be  introduced  into  the  flame  by 
means  of  a  wire,  we  obtain,  if  K9  Na  and  Li  are  present,  the 
characteristic  reaction  of  these  three  bodies  simultaneous  or 
successively.  If  calcium  and  strontium  be  also  present  their 
spectra  usually  first  appear  after  K,  Na  and  Li  have  been 
vaporized.  The  reaction  of  these  metals  fails  with  weak  con- 
tents of  calcium  and  strontium;  we  obtain  it,  however,  imme- 
diately if  we  introduce  the  wire  for  a  few  moments  into  the 
reducing  part  of  the  flame,  moisten  it  with  hydrochloric  acid, 
and  bring  it  again  into  the  flame. 

All  these  tests,  as  the  heating  of  it  alone,  or  with  hydro- 
chloric acid,  the  treatment  with  ammonium  fluoride  alone,  or 
with  sulphuric  and  hydrochloric  acid,  provide  the  mineralogist 

116 


KADI  ATI  ON   AND   ABSORPTION. 

and  still  more  the  geologist  with  a  series  of  highly  simple  tests 
for  determining  many  substances  occurring  in  nature  even  in 
the  smallest  particle,  such,  for  example,  as  the  minerals  so 
similar  to  one  another,  consisting  of  double  silicates,  contain- 
ing lime,  with  a  certainty  which  is  scarcely  attainable  with  an 
abundant  supply  of  material  by  means  of  an  extended  and  pro- 
tracted analysis.  Some  examples  will  illustrate  this  best. 

1.  A  drop  of  sea-water  evaporated  on  a  platinum  wire  showed 
a  strong  sodium  reaction,  and  after  volatilizing  the  chloride  of 
sodium  a  weak  calcium  reaction  which,  by  moistening  the  wire 
with  hydrochloric  acid,  became  for  a  moment  very  brilliant. 
If  we  treat  a  few  decigrams  of  the  residue  of  sea-water,  in  the 
way  described  for  lithium,  with  sulphuric  acid  and  alcohol  we 
easily  obtain  the  reaction  of  potassium  and  lithium.     The  pres- 
ence of  strontium    in  sea- water   can  be  observed  best  in   the 
boiler   crusts  of   steamships.     The   filtered   hydrochloric  acid 
solution  of  the  same  leaves,  on  evaporation  and  solution  in  the 
smallest  quantity  of  alcohol,  a  dull  yellow  coloring  from   the 
basic  iron  salt  which  is  deposited  after  some  days  and  collected 
on  a  filter  and  washed  with  alcohol.     The  filter  burnt  on  a  fine 
platinum  wire  gives,  along  with  the   calcium  line,  a  complete 
and  bright  strontium  spectrum. 

2.  Mineral  waters  often  show  at  once  the  potassium,  sodium, 
lithium,  calcium,  and  strontium  reactions.     For  example,  if 
we  introduce  a  drop  of  Durkheim  or  Krauznach  mineral  water 
into  the  flame  we  obtained  the  lines  Na  a,  Li  a,  Ca  a,  and  Ca  /?.    If 
we  use  instead  of  the  mineral  water  a  drop  of  the  mother  liquid 
the  same  lines  appear  with  great  brilliancy.     In  proportion  as 
the  chloride  of   sodium  and   lithium  are  volatilized  and   the 
chloride  of  calcium  has  become  more  basic,  the  characteristic 
lines  of  the  strontium  spectrum  gradually  develop  themselves 
and,  becoming  brighter,  finally  are  seen  in  all  their  extent.     We 
obtain  here  also,  by  a  mere  glance  at  a  single  drop  vaporized  in 
the  flame,  the  complete  analysis  of  the  mixture  of  five  sub- 
stances in  a  few  moments. 

3.  The  ash  of  a  cigar  moistened  with  some  HC1  and  held  in 
the  flame  gives  the  lines  Naa,  Ka,  Li  a,  Caa,  Cap. 

4.  Potash  glass  of  a  combustion  tube  gave,  both  with   and 
without  hydrochloric  acid,   Na  a  and  K  a,    and   treated   with 

11? 


MEMOIRS    OK 

fluoride  of  ammonium  and  sulphuric  acid  Caa,  Cap  and  traces 
of  Li  a. 

5.  Orthoclase  from  Baveno  gives  either  alone  or  with  hydro- 
chloric acid  only  No,  a.  with  traces  of  K  a  and  Lia\  with  fluoride 
of  ammonium  and  sulphuric  acid  the  intense  line  Naa,  K  a  and 
somewhat  less  distant  Li  a.     After  volatilizing  the  constituents 
thus  observed  the  bead  introduced,  into  the  flame  with  HCl, 
gives  only  a  scarcely  distinguishable  flash  of  the  lines  Caa  arid 
Cap.     The  residue  remaining  on  the  platinum  wire  after  this 
test  showed,  when  moistened  with  cobalt  solution  and  heated, 
the  characteristic  color   of   alumina.     If  we  employ  the  well- 
known  reaction  of  silicic  acid  also  it  follows  from  this  examina- 
tion, made  in  a  few  minutes,  that  the  orthoclase  from  Baveno 
contains  silicic,  alumina,  potash  with  traces  of  soda,  lime  and 
lithia  whilst  every  trace  of  baryta  and  strontia  fail. 

6.  Adularia  from  the  Gotthard  conducted  itself  quite  similar 
to  the  orthoclase  from  Baveno  only  that  the  lithium  reaction 
fulled  entirely  and  the  calcium  reaction  nearly  so. 

7.  Labradorite  from  St.  Paul  gives,  by  itself,  only  the  sodium 
line  Na  a  and  not  the  calcium  spectrum.     But  the  sample  moist- 
ened with  hydrochloric  acid  gives  the  calcium  lines  CWand 
Cap  very  brilliantly.     With   the  test  by  means  of   fluoride  of 
ammonium  we  still  obtain  a  weak  potassium  reaction  and  very 
faint  traces  of  lithium. 

8.  Labradorite  from  the  Diorite  of  Corsica  comported  itself 
similarly  only   that   the  traces  of   the  lithium  reaction  were 
wanting. 

9.  Mosanderite  from  Brevig  and  Tscheffkinite  from  thellmen 
mountains  gave  by  itself  only  the  sodium  reaction,  but  the  cal- 
cium line  Caa  and  Cap  when  treated  with  hydrochloric  acid. 

10.  Melinophane   from  Lamoe  gave  by  itself  only  Naa  but 
with  hydrochloric  acid  Caa,  Cap  and  Li  a. 

11.  Scheelite  and   Sphene  gave,  on  treatment  with  hydro- 
chloric acid,  the  very  brilliant  calcium  reaction. 

12.  If  small  quantities  of  strontium  are  present  with  calcium 
we  employ  the  line  Sr6  most  advantageously  to  detect  the  for- 
mer.    By  means  of  the  same  it  is  easy  to  detect  a  small  content 
of  strontium  in  very  many  sedimentary  limestones.     Na  a,Li  a 
R  a  particularly  Li  a  are  shown  immediately  on    heating  the 

118 


KAUIATION  AND   ABSORPTION. 

limestone  in  the  flame.  Those  minerals,  converted  into  cal- 
cium chloride  by  hydrochloric  acid  and  introduced  into  the 
flame  in  this  form,  give  the  same  lines  and  besides  frequently 
the  line  Sr  6  quite  distinctly.  But  this  appears  only  for  a  short 
time  and  most  distinctly  whilst  it  is  being  developed  in  the 
course  of  the  volatilization  in  the  flame  and  shortly  before  the 
fading  out  of  the  calcium  spectrum. 

In  this  way  the  lines  Naa,  Li  a,  Ka,Caa,Cap,  Sr  6  were  found 
in  the  following  limestones  : — 

Silurian  limestone1  from  Kugelbad  near  Prague, 

Shell  limestone  from  Rohrbach  near  Heidelberg, 

Lias  limestone  from  Malsch  in  Baden, 

Chalk  from  England. 

The  following  limestones  showed  the  lines Naa,  Lia,  Ka,Caa, 
Cap, without  the  blue  strontium  line: — 

Marble  from  the  granite  of  Auerbach,2 

Devonian  limestone  from  Gevolstein  in  the  Eifel, 

Carboniferous  limestone  from  Planite  in  Saxony, 

Dolimite  from  Nordhausen  in  the  Hartz, 

Jura  limestones  from  the  Streitberg  in  Franconia. 

We  now  see  from  these  few  experiments  that  extended  and 
careful  spectral  analysis  of  the  lithium,  potassium,  sodium, 
and  strontium  content  of  various  limestone  formations  are  of 
the  greatest  geological  interest  with  respect  to  their  order  of 
formation  and  their  local  disposition  and  may  possibly  lead  to 
unexpected  conclusions  on  the  nature  of  the  earlier  ocean  and 
sea  basins  in  which  the  formation  of  these  minerals  took  place. 

BARIUM. 

The  spectrum  of  barium  is  the  most  complicated  of  the 
spectra  of  the  alkalis  and  alkaline  earths.  It  is  distin- 
guished at  the  first  glance  from  those  heretofore  examined  by 

1  The  lithium  line  could  not  be  detected  with  certainty  in  this  class  of 
minerals,  the  line  Sr  <5  on  the  contrary  was  very  strong. 

2  By  means  of   the  experiment  with   alcohol  above  described  enough 
nitrate  of  strontium  was  obtained  from  twenty  grams  of  marble  to  pro- 
duce a  bright  and  complete  spectrum  of   strontium.     Whether  the  re- 
maining limestones  treated  in   this  way  show  a  strontium  content  we 
have  not  investigated. 

119 


MEMOIRS     ON 

the  green  lines  Ba  a  and  Bap,  which  exceed  all  the  others  in 
brilliancy, appearing  first  and  disappearing  last  in  weak  reac- 
tions. Ba  y  is  less  distinct  but  is  still  always  to  be  treated  as  a 
characteristic  line.  The  relatively  great  extension  of  its  spec- 
trum is  the  reason  why  the  spectral  reaction  of  the  barium  com- 
pounds is  somewhat  less  delicate  than  those  of  the  substances 
heretofore  examined.  0.3  grams  of  chlorate  of  barium 
burned  in  onr  room  with  milk  sugar  gave,  after  the  air  had 
been  thoroughly  mixed  by  moving  an  open  umbrella,  the  line 
Ba  a  most  distinctly,  for  a  long  time.  We  may  therefore  con- 
clude from  a  calculation  made  similar  to  that  for  sodium,  that 
the  reaction  will  show,  with  perfect  distinctness,  not  less  than 
TTJ^oth  of  a  milligram. 

Chloride,  bromide,  iodide,  and  fluoride  of  barium,  the  hy- 
drated  oxide,  the  sulphate,  and  the  carbonate,  give  the  reac- 
tion most  markedly  and  can  therefore  be  determined  by 
immediate  heating  in  the  flame. 

Silicates  decomposable  by  hydrochloric  acid  containing  ba- 
rium give  the  reaction,  if,  as  indicated  in  the  case  of  lime,  they 
are  introduced  into  the  flame  with, a  drop  of  hydrochloric  acid. 
Thus,  for  example,  barytharmotome  treated  in  this  way  gives 
the  line  Caa  Cap  along  with  the  lines  Baa.Bap. 

Compounds  of  barium  with  non-volatile  acids,  which  are 
indifferent  with  or  without  hydrochloric  acid  in  the  flame,  we 
may  fuse  best,  in  the  way  given  for  strontium,  with  carbonate  of 
sodium  and  then  test  the  carbonate  of  barium  thus  obtained.  If 
in  such  compounds  Ca,  Ba  and  Sr  occur  together  in  very  unequal 
amounts,  we  dissolve  in  a  drop  of  sulphuric  acid  the  carbonates 
obtained  by  fusion  and  extract  the  salt  with  alcohol  from  the 
evaporated  residue.  The  residue  then  contains  only  barium  and 
strontium  both  of  which  may  be  easily  detected  if  they  do 
not  occur  in  too  unequal  quantities.  When  it  is  desired  to  test 
for  the  smallest  traces  of  Sr  or  Ba,  we  transform  the  residue, 
by  heating  with  sal  ammoniac,  into  chlorides,  from  which  the 
chloride  of  strontium  can  be  easily  extracted  in  a  sufficiently 
concentrated  state  for  detection  by  means  of  alcohol.  If  neither 
of  the  substances  to  be  tested  is  present  in  very  small  quantities 
all  such  methods  of  separation  are  quite  unnecessary,  as  the 
following  experiment  shows: — a  mixture  of  sodium,  potassium, 

120 


RADIATION  AND    ABSORPTION. 

lithium,  calcium,  strontium,  and  barium  chlorides  which  con- 
tained iUh  of  a  milligram  of  each  of  these  six  substances  at  the 
most,  was  introduced  into  the  flame  and  observed.  At  first 
the  brilliant  sodium  line  Naa  appeared  on  the  background  of 
a  weak  continuous  spectrum.  As  soon  as  this  began  to  fade 
away,  the  sharply  defined  brilliant  red  line  of  lithium  Li  a  ap- 
peared and  on  the  same  side  of  the  sodium  line,  still  farther 
away,  the  faint  potassium  line  Ka  whilst  the  barium  lines  Baa 
and  Ba  p  appeared  very  distinctly  in  their  characteristic  position 
and  peculiar  shade.  Whilst  the  compounds  of  potassium, 
lithium,  and  barium  were  slowly  volatilized  their  lines  faded 
away,  or  vanished  again  gradually  in  succession  until,  after  a 
few  minutes,  the  lines  Caa  Cap  and  Sra  /bV/s  Sr%  Sr  6  became 
visible  out  of  the  less  and  less  prominent  lines  of  strontium,  as 
from  a  dissolving  view,  in  all  their  characteristic  form,  shade 
and  position,  and  then  faded  away  and  entirely  vanished  after 
a  very  long  time. 

The  absence  of  any  one  or  more  of  these  components  could 
be  instantly  detected,  in  the  observation,  by  the  absence  of  the 
corresponding  lines. 

For  those  who  have  become  familiar  with  the  individual 
spectra  by  repeated  observation,  an  accurate  measurement  of 
the  individual  lines  is  unnecessary;  their  color,  their  relative 
position,  their  characteristic  definition  and  shade,  the  grada- 
tion in  their  brilliancy,  are  criterions  which  are  quite  sufficient 
for  definite  recognition  even  for  the  inexperienced.  These 
characteristics  may  be  compared  with  the  distinguishing  fea- 
tures which  the  various  precipitates  present  in  their  outward 
appearance,  which  we  use  as  a  reaction  test.  Just  as  the  char- 
acter of  a  precipitate  determines  whether  it  be  gelatinous,  pul- 
verulent, flocculent,  granular  or  crystalline,  so  also  the  spectral 
lines  indicate  their  characteristics  in  the  sharpness  of  their 
edges,  in  the  shading  off  uniformly  or  irregularly  on  one  or  both 
sides,  or  in  their  broader  or  narrower  appearance,  as  the  case 
may  be.  And  just  as  we  use  only  those  precipitates  in  analysis 
which  can  be  produced  by  the  greatest  possible  dilution,  so  we 
also  use  in  spectrum  analysis  for  this  purpose  only  those  lines 
which  require  for  their  production  the  smallest  amount  of  the 

121 


MEMOIKS   ON 

substance  and  only  a  moderately  high  temperature.  In  such 
characteristics  therefore  the  two  methods  are  quite  similar. 
On  the  contrary  spectrum  analysis  furnishes,  in  the  color  phe- 
nomena used  in  the  reaction,  a  property  which  gives  it  unlimited 
advantage  over  every  other  method  of  analysis.  Most  of  the 
precipitates  which  are  used  for  the  detection  of  substances  are 
white  and  only  a  few  colored.  Further  the  tint  of  the  latter  is 
not  very  constant  and  considerably  differentiated  according  to 
the  greater  or  less  condensed  state  of  the  precipitate.  Often 
the  smallest  mixture  of  a  foreign  substance  is  sufficient  to  oblit- 
erate completely  a  characteristic  color.  Small  differences  of 
color  of  the  precipitate  can  therefore  be  no  longer  used  as  a 
chemical  test.  In  spectrum  analysis,  on  the  contrary,  the  colored 
bands  remain  undisturbed  by  such  foreign  influences  and  are 
undisturbed  by  the  presence  of  other  bodies.  The  positions 
which  they  have  in  the  spectrum  determine  a  chemical  charac- 
teristic which  is  of  as  unalterable  and  fundamental  a  nature  as 
the  atomic  weight  of  the  substance,  and  therefore,  permits  us 
to  determine  it  with  an  almost  astronomical  exactness.  What, 
however,  gives  to  the  spectral  analytical  method  a  peculiar  im- 
portance, is  the  fact  that  it  almost  infinitely  exceeds  the  limits 
to  which  chemical  analysis  of  matter  has  heretofore  reached. 
It  predicts  for  us  the  most  valuable  conclusions  on  the  distribu- 
tion and  arrangement  of  geological  substances  in  their  forma- 
tion. Already  the  few  investigations,  which  this  memoir 
contains,  lead  to  the  unexpected  conclusion  that  not  only 
potassium  and  sodium  but  also  lithium  and  strontium  must  be 
counted  among  the  substances  of  the  earth  most  widely  scat- 
tered, though  only  in  minute  quantities. 

Spectrum  analysis  will  also  play  a  not  less  important  part  in 
the  discoveries  of  elements  not  yet  detected.  For  if  there  are 
substances  which  are  so  sparsely  scattered  in  nature  that  the 
methods  of  analysis  heretofore  used  in  observing  and  separating 
them  fail,  we  may  hope  to  detect  and  determine  many  of  them, 
by  the  simple  examination  of  their  spectra  in  flames,  which 
would  escape  the  ordinary  method  of  chemical  analysis.  That 
there  are  actually  such  elements  heretofore  unknown  we  have 
.already  had  an  opportunity  of  showing.  We  believe  that  we 
shall  be  able  yet  to  declare  with  absolute  certainty,  supported 

122 


RADIATION   AND   ABSORPTION. 

by  the  unquestioned  results  of  spectral  analytical  methods  that 
besides  potassium,  sodium  and  lithium,  there  is  still  a  fourth 
metal  belonging  to  the  alkali  group  which  will  give  quite  as 
characteristic  a  spectrum  as  lithium — a  metal  which  shows, 
with  our  spectral  apparatus,  only  two  lines,  a  weak  blue  line, 
which  almost  coincides  with  the  strontium  line  Srd  and  another 
blue  line,  which  lies  only  a  little  farther  toward  the  violet  end 
of  the  spectrum,  rivaling  in  intensity  and  distinctness  the  lith- 
ium line. 

On  the  one  hand  spectrum  analysis  offers,  as  we  believe  we 
have  already  shown,  a  means  of  wonderful  simplicity  for  de- 
tecting the  slightest  traces  of  certain  elements  in  terrestrial 
substances,  and  on  the  other,  it  opens  up  to  chemical  investi- 
gation a  field  heretofore  completely  closed,  which  extends  far 
beyond  the  limit  of  the  earth  even  to  our  solar  system  itself. 
Since,  by  the  analytical  method  under  discussion,  it  is  sufficient 
simply  to  see  the  gas  in  an  incandescent  state  in  order  to  make 
an  analysis,  it  at  once  follows  that  the  same  is  also  applicable  to 
the  atmosphere  of  the  sun  and  the  brighter  fixed  stars.  A  modi- 
fication with  respect  to  the  light  which  the  nucleus  of  these 
heavenly  bodies  radiate  must  be  introduced  here.  In  a  memoir 
"On  the  Relation  between  the  Emission  and  the  Absorption  of 
Bodies  for  Heat  and  Light  "  1  one  of  us  has  proven,  by  theo- 
retical considerations,  that  the  spectrum  of  an  incandescent  gas 
is  reversed,  that  is,  that  the  bright  lines  are  transformed  into 
dark  ones  when  a  source  of  light  of  sufficient  intensity, 
which  gives  a  continuous  spectrum,  is  placed  behind  the  same. 
From  this  we  may  conclude  that  the  sun's  spectrum,  with  its 
dark  lines,  is  nothing  else  than  the  reversal  of  the  spectrum 
which  the  atmosphere  of  the  sun  itself  would  show.  Hence  the 
chemical  analysis  of  the  sun's  atmosphere  requires  only  the 
examination  of  those  substances  which,  when  brought  into  a 
flame,  produce  bright  lines  which  coincide  with  the  dark  lines 
of  the  solar  spectrum. 

In  the  article  mentioned,  the  following  examples  are  given 
as  experimental  proof  of  the  theoretically  deduced  law  referred 
to: 

1    Kirchhoff,  Pog£.  Ann.  Vol.  CIX  p.  275.     See  previous  memoir. 

123 


MEMOIRS     ON 

The  bright  red  line  in  the  spectr-um  of  a  flame  in  which  a 
bead  of  chloride  of  lithium  is  introduced  is  changed  into  a 
black  line  when  we  allow  full  sunlight  to  pass  through  the 
flame. 

If  we  substitute  for  the  bead  of  lithium  one  of  sodium  chlo- 
ride, the  dark  double  line  D  (which  coincides  with  the  bright 
sodium  line)  shows  itself  in  the  sun's  spectrum  with  unusual 
brilliancy. 

The  dark  double  line  D  appears  in  the  spectrum  of  the  Drum- 
mond's  light  if  we  pass  its  rays  through  the  flame  of  aqueous 
alcohol,  into  which  we  have  introduced  chloride  of  sodium.1 

It  will  not  be  without  interest  to  obtain  still  further  confir- 
mations of  this  remarkable  theoretical  law.  We  may  arrive  at 
this  by  the  investigation  which  will  now  be  described. 

We  made  a  thick  platinum  wire  incandescent  in  a  flame  and 
by  means  of  an  electric  current  brought  it  nearly  to  its  melting 
point.  The  wire  gave  a  brilliant  spectrum  without  any  trace 
of  bright  or  dark  lines.  If  a  flame  of  very  aqueous  alcohol  in 
which  common  salt  was  dissolved  were  introduced  between  the 
wire  and  the  slit  of  the  apparatus,  the  dark  line  D  showed  it- 
self with  great  distinctness. 

We  can  produce  the  dark  line  D  in  the  spectrum  of  a  platinum 
wire  which  has  been  made  incandescent  by  a  flame  if  we  merely 
hold  before  it  a  test  tube  into  which  some  sodium  amalgam  has 
been  introduced,  and  then  heat  it  to  boiling.  This  investiga- 
tion is  important,  on  this  account,  in  that  it  shows  that  far 


1  In  the  March  number  of  the  Philosophical  Magazine  for  1860 
Stokes  calls  attention  to  the  fact  that  Foucault  had  made  already  an 
observation  in  1849  which  is  similar  to  that  mentioned  above.  In  the 
examination  of  the  electric  arc  between  two  carbon  points  he  observed 
(1,  Institut  1849,  p.  45)  that  in  the  spectrum  the  same  bright  lines  were 
present  in  the  position  of  the  double  line  D  of  the  solar  spectrum,  and 
that  the  dark  line  D  of  the  arc  is  intensified,  or  produced,  if  we  allow 
the  rays  of  the  sun  or  one  of  the  incandescent  points  to  pass  through  it 
and  then  resolve  them  in  the  spectrum.  The  observation  mentioned 
in  the  text  gives  the  explanation  of  this  interesting  phenomena  already 
observed  by  Foucault  eleven  years  before  and  shows  that  the  same  is  not 
influenced  by  the  peculiarity  of  the  electric  light,  which  is  still,  from 
many  points  of  view,  so  enigmatical,  but  arises  from  a  sodium  compound 
which  is  contained  in  the  carbon  and  is  transformed  by  the  current  into 
incandescent  gas. 

124 


RADIATION    AND    ABSORPTION. 

below  the  point  of  incandescence  of  sodium  vapor,  its  absorbent 
effect  is  exercised  exactly  in  the  same  parts  of  the  spectrum 
as  with  the  highest  temperatures  which  we  are  able  to  produce 
and  at  which  that  of  the  solar  atmosphere  exists. 

We  have  been  able  to  reverse  the  bright  lines  of  the  spectra 
of  K,  Sr,  Ca,  Ba  by  the  employment  of  sunlight  and  mixtures 
of  the  chlorates  of  these  metals  with  milk  sugar.  Before  the 
slit  of  the  apparatus  a  small  iron  trough  is  placed;  into  this  the 
mixture  was  introduced,  and  the  full  sunlight  passed  along 
the  trough  to  the  slit  and  the  mixture  ignited  on  one  side  by  an 
incandescent  wire.  The  telescope  was  set  with  the  intersection 
of  its  cross  hairs,  which  were  mounted  at  an  acute  angle  with 
one  another,  on  the  bright  line  of  the  flame  spectrum,  the 
reversal  of  which  was  to  be  tested;  the  observer  concentrated 
his  attention  on  this  point  in  order  to  judge  whether  at  the 
moment  of  ignition  a  dark  line  was  visible,  passing  through 
the  intersection  of  the  cross  hairs.  In  this  way  it  was  quite 
easy  with  the  proper  proportion  of  the  mixture,  to  be  burnt,  to 
establish  the  reversal  of  the  lines  Ba  a  and  Ba  ft  and  the  line 
K  /3.  The  last  of  these  coincided  with  one  of  the  most  distinct 
lines  of  the  solar  system,  although  not  indicated  by  Fraunhofer; 
this  line  appeared  much  more  distinctly  at  the  moment  of  ig- 
nition of  the  potash  salt  than  otherwise.  In  order  to  observe 
the  reversal  of  the  bright  lines  of  the  strontium  spectrum  in  the 
way  described,  the  chlorate  of  strontium  must  be  dried  in  the 
most  careful  manner;  a  slight  trace  of  moisture  causes  the  sun's 
rays  to  be  weakened  and  produces  the  positive  spectrum  of 
strontium  on  account  of  the  flame  becoming  filled  with  salt 
particles  which  have  been  spattered  about  by  the  ignition. 

"We  have  limited  ourselves  in  this  memoir  to  the  investiga- 
tion of  the  spectra  of  the  metals  of  the  alkalis  and  alkaline 
earths,  and  these  only  in  so  far  as  was  necessary  for  the  analysis 
of  terrestrial  matter.  We  reserve  for  ourselves  the  further 
extension  of  these  investigations  which  are  desirable  in  connec- 
tion with  the  analysis  of  terrestrial  substances  and  the  analysis 
of  the  atmospheres  of  the  stars. 
Heidelberg,  April,  1860. 


125 


MEMOIRS  ON  RADIATION  AND   ABSORPTION. 
BIOGRAPHICAL  SKETCH. 

ROBERT  WILHELM  BUNSEN  was  born  in  Gottingen  March  15, 
1811.  He  received  his  doctor's  degree  in  1830  and  became 
private-decent  in  1833  in  that  University.  In  1836  he  became 
Professor  of  Chemistry  in  the  Polytechnic  School  at  Cassel  and 
in  1838  accepted  a  similar  position  in  the  University  of  Mar- 
burg. In  1851  he  went  to  Breslau  and  the  following  year  to 
Heidelberg,  where  he  remained  until  his  death.  Both  as  a 
teacher  and  as  an  investigator,  he  was  one  of  the  most  eminent 
of  his  generation,  making  many  important  contributions  to 
both  Physics  and  Chemistry.  His  spectroscope,  photometer, 
calorimeter,  gas  burner,  filter  pump,  battery,  etc.,  on  the  one 
hand,  and  his  early  contributions  to  organic  chemistry,  the 
methods  of  gas  analysis,  photochemical  action,  etc.,  on  the 
other,  illustrate  the  versatility  of  his  genius.  His  work  in  con- 
nection with  his  colleague,  Kirchhoff,  resulted  in  one  of  the 
most  brillant  achievements  of  the  century, — the  application  of 
the  spectroscope  to  the  analysis  of  terrestrial  substances, — 
which  revealed  at  once  several  new  elements  and  showed  the 
common  constitution  of  all  bodies  in  the  stellar  system.  His 
final  contribution  was  made  in  1887  after  an  illustrious  scientific 
career  of  nearly  sixty  years.  During  his  last  years  he  was  a 
familiar  figure  on  the  streets  of  Heidelberg,  in  which  city  he 
died  Aug.  15,  1899. 


136 


BIBLIOGRAPHY. 

Brief  list  of  publications  of  historical  importance. 

NEWTON.     [Radiation.]  Phil.  Trans,  p.  827.  1701 

PICTET.     Essai  sur  le  Feu.  1791 

PREVOST.     Recherches  sur  la  Chaleur,  Jonr.  de  Phys.     1792 
PREVOST.     Du  Calorique  Rayonnant,  8  Geneva.  1809 

PREVOST.     Sur  la  Transmission  du  Calorique,  etc.,   Jour. 

de  Phys.  de  Chim.  1811 

HERSCHEL,  W.      [Radiations   beyond    spectrum.]    Phil. 

Trans.  1800 

LESLIE,  J.      Inquiry    into    the    Nature,    etc.,  of  Heat. 

London.  1804 

RUMFORD.     Memoires  snr  la  Chaleur.  Paris.  1804 

DELAROCHE.     Obser.  sur  la  Calorique  Rayonnant,  Journ. 

de  Phys.  de  Chim.  1812 

FOURIER.     Sur  la  Chaleur  Rayonnant   Journ.  de  Phys. 

de  Chim.  1817 

DULONG  ET  PETIT.     [Law   of   Cooling.]  Ann.  de  Chim, 

et  de  Phys.  1818 

HERSCHEL,  J.     [Spectra  of  Colored  flames.]  Ed  in.  Phil. 

Trans.  1822 

FRAUNHOFER.     [Spectra     of    flames]     Gilbert's    Ann. 

1823,  Harper's  Series  II.  1898 

TALBOT.     [Spectra   of  flames.]    Brewster's  Jour,  of  Sci. 

1826 
MELLONI.     Sur  la  transmission  de  la  chaleur  Rayonnant, 

etc.,  Ann.  de  Chim.  et  de  Phys.  1833-37-39 

MELLOXI.     La  Thermochrose   ou  la   Coloration  Calori- 
que, Naples.  1850 
DE   LA  PROVOSTAYE  ET  DESAINS.     [Law    of   Cooling.] 

Ann.  de  chim.  et  de  Phys. 
127' 


MEMOIRS    ON  RADIATION  AND   ABSORPTION. 

DE  LA  PROVOSTAYE  ET  DESAINS.     [Relation  of  Absorp- 
tion and  Emission.]  Ann.  de  Chim.  et  de  Phys.      1853 
DRAPER,  J.     [Law  of  Draper.]  Phil.  Mag.  1847 

DRAPER,  J.     [Max,  Solar  Energy.]  Phil.  Mag.  1857 

FOUCAULT.     [Reversal  of  D  lines.]  Soc.  Philomatiqne    1849 
STOKES.     [Note    on     Foucault    and   KirchhofFs    Obs.] 

Phil.  Mag.  March.  1860 

STEFAN.     [Stefan's  Law.]  Wien.  Akad.  Ber.  1879 

LANGLEY.     Researches  on  Solar  Heat.  Washington.         1884 
BOLTZMANN.      [Deduction    of    Stefan's   Law.]      Wied. 

Ann.  XXII.  1884 

WIEDEMANN,  E.     [Luminescence    of    Vapors.]     Wied. 

;,  ;  ( 1879 

Ann.  •<  1889 

(1895 

RAYLEIGH.     [Radiation  and  Molecular  Motions.]    Phil. 

Mag.  1889 

WEBER,  H.  F.  [Weber's  Law  A  Jftf  =  const.]  Berl.  Akad. 

Ber.  1888 

WIEN.  [Laws  of  Displacement,  Emission,  etc.]  Wied. 

Ann.  j  1894 

(1896 
PLANCK.  [Law  of  Emission.]  Ber.  Deut.  Phys.  GeselL 

Oct.  1900 


128 


INDEX. 


A 

Absorption  and  Radiation,  Relation  of        ....  40 

Assumption  made  in  establishing  Kirchhoff's  law      .        .  76 

Alum,  Observation  on    .       . 27 

B 

Barium,  Observations  on 119 

Bath,  Description  of 25 

Black  bodies,  Proof  of  law  of  radiation  for         .        .  78 

Bunsen,  Biography  of 126 

C 

Calcium,  Observations  on 115 

Caloric,  Nature  of 17 

"  Clausins' "  law '••«,.•        .        .  94 

Cold,  Reflection  of 7 

Conduction  and  Radiation,  Relation  of     ....  49 

D 

Diathermancy,  Table  of 37 

"              General 69 

Distance,  Law  of            9 

Draper's  law 95 

Dulong  and  Petit's  law  ........  67 

E 

Emissive  and  Absorptive  power 75 

Equilibrium  of  heat,  Meaning  of  the 4 

F 

Fluids,  Radiant  and  non-radiant         .....  12 

Foucault,  Observations  of    .    ' .    .        .        .         .        .        .  124 

129 


INDEX. 

G 
Glass,  Observations  on         .  .        .        .        .  26-29-12 

H 

Heat,  Conduction  of    ...'..         .  12 

Absolute  and  relative  equilibrium  of        ...  7 

"      Nature  of      .        . 4 

Helmholtz,  Law  of .        ;        .        ...        .        .        .  88 

High  temperatures,  Radiation  at 59 

K 

Kirchhoff,  Biography  of                97 

L 

Lampblack,  Use  of                         26 

Le  Luc,  Ideas  of /       .        .        .  3 

Le  Sage,  Theory  of        .        .        ..,.,.     ;.      ,.        .  4-17 

Leslie,  Observations  of         . 26 

Lithium,                       on        ......      •  »  r     •        .  109 

M 

Mercury,   Eadiations  from  .        ...        .        .        .  61 

Mica,  Observations  on  .        .        ,    •     . .       .        .        .        .  27-29-32 

Mutual  Radiations  of  black  bodies     .        |       , .       »        .  83 

P 

Pictet,  Experiments  of           .        ....    .'      .       ',        .        .  8 

Potassium,  Observations  on         .        .        .        .        .        .  42 

Prevost,  Biography  of 20 

Principles  and  Conclusions,  Resume  of       ....  18 

Q 

Quality  of  heat  radiated,  Experiments  on  .        .        .        .  33-34 

R 

Radiation  and  absorption,  Relation  of          ....  40 

"     from  polished  surfaces  and  lampblack  ...  26 

"     and  refractive  power,  Connection  between   .        .  42 

*'     and  conduction,  Relation  of 49 

"     for  different  thicknesses,  Law  of  .        .        .        .  29-31 

Radiant  Heat,  Second  Series 53 

Radiating  Substances,  Table  of 28 

Ratio  between  Emissive  and  absorptive  power  of  ajl  bodies  78 

130 


INDEX. 

Refractive  power  on  radiation,   Influence  of      ...  42 

Reflective        "• '  • 4<  "  "...  42 

Reversal  of  Spectra .          123 

Rock-salt,  Observations  on 28-30-33 

"        Quality  of  heat  radiated  from      ....  54 


Selenite,  Observations  on 27 

Sodium,  Observations  on 107 

Spectral  Observations            101 

Spectra  produced  by  spark    .  106 

Stewart,  Biography  of    ....         ....  72 

Strontium,  Observations  011 113 

Swan,  Observations  of 107 

T 

Temperature  and  Radiation,  Law  connecting    ...  64 

Temperature  of  different  flames 105 

Theory  of  exchanges,  Extension  of 23 

Thermo-multiplier,  Description  of 24 

Thick  and  thin  Plates,  Radiation  from        .  33-34 

Tourmaline,  Radiation  and  Absorption  of  ....  95 


131 


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interesting  descriptions  of  the  latest  phases  and  discoveries  of  the  science. 
In  contents  and  dress  it  is  an  attractive  volume,  well  suited  for  its  use. 

DANA'S  REVISED  TEXT-BOOK  OF  GEOLOGY  .  .  .  $1.40 
Fifth  Edition,  Revised  and  Enlarged.  Edited  by  WILLIAM  NORTH 
RICE,  Ph.D.,  LL.D.,  Professor  of  Geology  in  Wesleyan  University. 
This  is  the  standard  text-book  in  geology  for  high  school  and  elementary 
college  work.  While  the  general  and  distinctive  features  of  the  former 
work  have  been  preserved,  the  book  has  been  thoroughly  revised,  enlarged, 
and  improved.  As  now  published,  it  combines  the  results  of  the  life 
experience  and  observation  of  its  distinguished  author  with  the  latest 
discoveries  and  researches  in  the  science. 

DANA'S  MANUAL  OF  GEOLOGY $5.00 

Fourth  Revised  Edition.  This  great  work  is  a  complete  thesaurus  of 
the  principles,  methods,  and  details  of  the  science  of  geology  in  its 
varied  branches,  including  the  formation  and  metamorphism  of  rocks, 
physiography,  orogeny,  and  epeirogeny,  biologic  evolution,  and  paleon- 
tology. It  is  not  only  a  text-book  for  the  college  student  but  a  hand- 
book for  the  professional  geologist.  The  book  was  first  issued  in  1862, 
a  second  edition  was  published  in  1874,  and  a  third  in  1880.  Later 
investigations  and  developments  in  the  science,  especially  in  the  geology 
of  North  America,  led  to  the  last  revision  of  the  work,  which  was  most 
thorough  and  complete.  This  last  revision,  making  the  work  substantially 
a  new  book,  was  performed  almost  exclusively  by  Dr.  Dana  himself,  and 
may  justly  be  regarded  as  the  crowning  work  of  his  life. 


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(177) 


Astronomy 


NEWCOMB'S  ELEMENTS  OF  ASTRONOMY 

Cloth,    12mo,  240  pages.      Illustrated          .         .         .  $1.00 

By   SIMON    NEWCOMB,  Ph.D.,  LL.D.,  Late  Professor  of  Mathe- 
matics and  Astronomy,  Johns   Hopkins  University,  and  formerly 
Senior  Professor  of  Mathematics,  United  States  Navy. 
This   volume   has   been    prepared    for   use   in   High    Schools   and 
College   Preparatory  Schools.     The  facts  and  laws  of  the  science  have 
been  condensed  within  small  compass,  and  the  subject  is  so  presented 
that  but  little  of  formal  mathematics  is  necessary  in  its  study.     A  brief 
history  of  astronomy  is  included,  with  a  General  Index  for  convenient 
reference,  and  numerous  illustrations,  figures,  and  diagrams. 

TODD'S  NEW  ASTRONOMY 

Cloth,  12mo,  480  pages.     Illustrated $1.30 

By   DAVID  P.  TODD,  M.A.,  Ph.D.,  Professor  of  Astronomy   and 

Director  of  the  Observatory,  Amherst  College. 

The  noteworthy  feature  which  distinguishes  this  from  other  text- 
books on  astronomy  is  the  practical  way  in  which  the  subject  is  taught, 
largely  by  laboratory  experiments  and  observation  methods.  By  laying 
more  stress  on  the  physical  than  on  the  mathematical  facts  of  astronomy 
the  author  has  made  the  book  deeply  interesting.  The  marvelous  dis- 
coveries of  astronomy  in  recent  years  are  all  described,  while  the 
numerous  original  and  ingeniously  devised  illustrations  and  diagrams 
form  an  important  feature  of  the  book. 

BOWEN'S  ASTRONOMY  BY  OBSERVATION 

Boards,  Quarto,  94  pages .     $1.00 

By  ELIZA  A.  BOWEN. 

This  book,  unique  in  its  form  and  character,  and  original  in  its 
methods,  is  the  work  of  a  practical  teacher,  and  its  reasoning  always 
appeals  to  observation,  study,  and  thought.  Careful  directions  are 
given  when,  how,  and  where  to  find  the  heavenly  bodies  and  the 
student  is  assisted  in  his  search  by  helpful  star-maps. 

STEELE'S  POPULAR  ASTRONOMY 

Cloth,    12mo,  349  pages.     Illustrated  .         .         .         .     $1.00 

Revised   and  Brought  Down  to  Date   by  MABEL  LOOMIS  TODD, 

author  of  "  Corona  and  Coronet,"  "  Total  Eclipses  of  the  Sun,"  etc. 

This  is  a  revision  of  Steele's    Descriptive    Astronomy,   and  while 

it  preserves   all   the   highly    desirable  features  of  the  original    work   it 

constitutes  substantially  a  new  book.     The  revision  incorporates  all  the 

changes  and  additions  made  necessary  by  the  rapid  advance  of  practical 

and  physical  astronomy  in  the  last  fifteen  years,  and  contains  a  large 

number   of   excellent  illustrations  and  diagrams,  together  with    several 

color  plates  and  a  system  of  star-maps. 


Copies  sent,  prepaid,  to  any  address  on  receipt  of  the  price. 

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(180) 


Gray's  Series  of  Botanies 

By  the  late  ASA  GRAY,    LL.D.,  of  Harvard  University 


FOR  ELEMENTARY  AND  GRAMMAR  SCHOOLS 

Gray's  How  Plants  Grow.     With  a  Popular  Flora         .         .     $0  80 
A  simple  introduction  to  the  study  of  Botany. 

Gray's  How  Plants  Behave.     A  Botany  for  Young  People     .         .54 
A  primary  book  showing  how  plants  move,  climb,  act,  etc. 

FOR  SECONDARY  SCHOOLS 

Gray's  Lessons  in  Botany.     Revised  edition          .         .         .         .94 
Gray's  Field,  Forest,  and   Garden    Botany.      New   edition, 

containing  Flora  only    .         .         .         .         .         .         .       1 .44 

Gray's  School  and  Field  Book  of  Botany.     Comprising  the 

"Lessons"  and  "Field,  Forest,  and  Garden  Botany,"  1.80 
A  complete  book  for  school  use. 

FOR  COLLEGES  AND  ADVANCED  STUDENTS 

Gray's  Manual  of  Botany.      Revised,  containing  Flora  only. 

For  the  Northern  United  States,  east  of  the  Missisippi,  1.62 
The  Same.  Tourist's  edition.  Thin  paper,  flexible  leather,  2.00 
Gray's  Lessons  and  Manual  of  Botany.  One  volume.  Revised, 

comprising  the  "Lessons  in  Botany"  and  the  "  Manual,"  2.16 
Gray's  Botanical  Text-Book 

I.     Gray's  Structural  Botany 2.00 

II.     Goodale's  Physiological  Botany        ....       2.00 

FOR  WESTERN  STUDENTS 

Coulter's  Manual  of  the  Botany  of  the  Rocky  Mountains       .       1.62 
Gray   and    Coulter's  Text-Book  of  Western  Botany.     Com- 
prising Gray's  "Lessons"  and  Coulter's  "  Manual  of 
the  Rocky  Mountains"          .         .         *         .         »         .2.16 


Copies  of  any  of  the  above  books  will  be  sent,  prepaid,  to  any  address 
on  receipt  of  the  price  by  the  Publishers  : 

American   Book  Company 

NEW  YORK  *  CINCINNATI  •  CHICAGO 

(171) 


Biology  and  Zoology 


DODGE'S    INTRODUCTION    TO     ELEMENTARY     PRACTICAL 
BIOLOGY 

A  Laboratory  Guide  for  High  School  and  College  Students. 
By  CHARLES  WRIGHT  DODGE,  M.S.,  Professor  of  Biology 
in  the  University  of  Rochester  .  .  .  .  .  $1.80 

This  is  a  manual  for  laboratory  work  rather  than  a 
text-book  of  instruction.  It  is  intended  to  develop  in  the 
student  the  power  of  independent  investigation  and  to 
teach  him  to  observe  correctly,  to  draw  proper  conclusions 
from  the  facts  observed,  to  express  in  writing  or  by  means 
of  drawings  the  results  obtained.  The  work  consists 
essentially  of  a  series  of  questions  and  experiments  on 
the  structure  and  physiology  of  common  animals  and 
plants  typical  of  their  kind — questions  which  can  be 
answered  only  by  actual  investigation  or  by  experiment. 
Directions  are  given  for  the  collection  of  specimens,  for 
their  preservation,  and  for  preparing  them  for  examination; 
also  for  performing  simple  physiological  experiments. 

ORTON'S     COMPARATIVE     ZOOLOGY,     STRUCTURAL     AND 
SYSTEMATIC 

By  JAMES  ORTON,  A.M.,  Ph.D.,  late  Professor  of  Natural 
History    in    Vassar    College.      New    Edition    revised    by 
CHARLES  WRIGHT  DODGE,  M.S.,  Professor  of  Biology  in 
the  University  of  Rochester          .         .         .         .         .         .    $1.80 

This  work  is  designed  primarily  as  a  manual  of 
instruction  for  use  in  higher  schools  and  colleges.  It 
aims  to  present  clearly  the  latest  established  facts  and 
principles  of  the  science.  Its  distinctive  character  con- 
sists in  the  treatment  of  the  whole  animal  kingdom  as  a 
unit  and  in  the  comparative  study  of  the  development  and 
variations  of  the  different  species,  their  organs,  functions, 
etc.  The  book  has  been  thoroughly  revised  in  the  light 
of  the  most  recent  phases  of  the  science,  and  adapted  to 
the  laboratory  as  well  as  to  the  literary  method  of  teaching. 


Copies  of  either  of  the  above  books  -will  be  sent,  prepaid^  to  any  address 
on  receipt  of  the  price. 

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(167) 


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